/  ft 

.  L.  n . 

JUL  1  3  '33 


UNIVERSITY  OF  CALIFORNIA 
AT  LOS  ANGELES 


u.  s. 


DEPARTMENT  OF  ASTRONOMY 

UNIVERSITY  OF  CALIFORNIA. 

AT  LOS  ANGELES 

JUL  ,2  5  '32 


THE   SCIENCE   SERIES 

Edited  by  EDWARD  LEE  THORNDIKE,  Ph.D.,  and 
F.  E.  BEDDARD,  M.A.,  F.R.S. 


1.  The  Study  of  Man.     By  A.  C.  HADDON. 

2.  The  Groundwork  of  Science.     By  ST.  GEORGE  MIVART. 

3.  Rivers  of  North  America.    By  ISRAEL  C.  RUSSELL. 

4.  Earth  Sculpture,  or  ;  The  Origin  of  Land  Forms.    By  JAMES 

GEIKIE. 

5.  Volcanoes;  Their  Structure  and  Significance.    By  T.  G. 

BONNEY. 

6.  Bacteria.     By  GEORGE  NEWMAN. 

7.  A  Book  of  Whales.     By  F.  E.  BBDDARD. 

8.  Comparative  Physiology  of  the  Brain,  etc.  By  JACQUES  LOEB. 

9.  The  Stars.     By  SIMON  NEWCOMB. 

10.  The  Basis  of  Social  Relations.     By  DANIEL  G.  BRINTON. 

n.  Experiments  on  Animals.     By  STEPHEN  FACET. 

12.  Infection  and  Immunity.     By  GEORGE  M.  STERNBERG. 

13.  Fatigue.     By  A.  Mosso. 

14.  Earthquakes.     By  CLARENCE  E.  DUTTON. 

15.  The  Nature  of  Man.     By  ELIE  METCHNIKOFK. 

16.  Nervous  and  Mental  Hygiene  in  Health  and  Disease.     By 

AUGUST  FOREL. 

17.  The  Prolongation  of  Life.    By  ELIE  METCHNIKOFF. 

18.  The  Solar  System.     By  CHARLES  LAKE  POOR. 

19.  Heredity.     By  J.  ARTHUR  THOMPSON,  M.A. 

20.  Climate.     By  ROBERT  DECOUKCY  WARD. 

at.  Age,  Growth,  and  Death.     I'.y  CHARLES  S.  MINOT. 

12.  The  Interpretation  of  Nature.     By  C.  LLOYD  MORGAN. 

33.  Mosquito  Life.    By  EVELYN  GROESBRECK  MITCHELL. 

34.  Thinking,  Peeling,  Doing.     By  E.  W.  SCRIPTURE. 

35.  The  World's  Gold.     By  L.  DE  LAUNAV. 

26.  The  Interpretation  of  Radium.     By  F.  SODDY. 

For  list  of  works  in  preparation  see  end  of  this  volume. 


Ube  Science  Series 

EDITED   BV 

professor  3.  fflcfteen  CattcII,  A.B.,  pb.2>. 

AND 

.B.,  J.1R.S. 


THE  STARS 


JUL  1  3  *33          / 

THE  STARS 

A  STUDY  OF  THE  UNIVERSE 


BY 

SIMON    NEWCOMB 

RETIRED  PROFESSOR  U.  S.  NAVY 


"Hcec  sunt  fastigia  mundi" 


DEPARTMENT  OF  ASTRONOMY 

UNIVERSITY  OF  CALIFORNIA 

AT  LOS  ANGELES 


NEW  YORK 

G.  P.  PUTNAM'S  SONS 

LONDON 

JOHN  MURRAY 


COPYRIGHT.  IQOI 

BY 
SIMON  NEWCOMB 

Published  October,  1901 

Reprinted  February,  1902 ;  June,  1904  ;  September,  1904. 
October,  1906 ;  August,  1908  ;  March,  1910 


ttbc  *ntcfeerbocher  press,  «ew  florfc 


Library 


N43* 


PREFACE 


WHEN  the  author  accepted  the  flattering  invita- 
tion of  the  editor  to  prepare  a  volume  for  the 
present  "  Science  Series,"  he  supposed  that  it  would 
be  an  easy  task  to  sketch  in  simple  language  for  the 
lay  as  well  as  the  scientific  reader  the  wonderful  ad- 
vances of  our  generation  in  the  knowledge  of  the 
fixed  stars.  But,  as  the  work  went  on,  it  became 
more  evident  at  every  step  that  such  was  not  the 
case.  The  problem  was,  now  to  study  whole  chapters 
of  observations  and  researches  on  some  minute  branch 
of  the  subject,  and  condense  their  gist  into  a  few  sen- 
tences ;  now  to  search  volumes  of  periodicals,  perhaps 
in  vain,  to  find  who  was  first  in  some  field,  or  what 
result  some  investigator  had  reached ;  now  to  do 
justice  to  the  respective  works  of  students  of  the 
same  subject ;  now  to  recast  or  rewrite  passages  in  the 
light  of  some  newly  published  research.  The  author 
must  say  in  all  candour  that  he  has  failed  to  sur- 
mount the  difficulties  thus  arising  in  a  way  satisfactory 
to  himself,  and  that  in  consequence  the  professional 
reader,  if  any  such  shall  take  up  the  book,  will  find 
defects  that  may  seem  to  him  serious  in  nearly  every 

iii 

2(11823 


iv  PREFACE 

chapter.  In  palliation  can  be  only  pleaded  the  extent 
and  complexity  of  the  subject,  and  the  impossibility 
of  entering  far  into  technical  details  in  a  work  de- 
signed mainly  for  the  general  use. 

In  treating  such  a  subject  it  is  impossible  always 
to  avoid  the  use  of  language  more  or  less  technical, 
except  at  the  expense  of  precision  and  completeness 
of  statement.  An  effort  has  however  been  made 
to  limit  the  use  of  such  language  to  the  necessities 
of  the  case. 

The  most  gratifying  experience  associated  with  the 
work  has  been  the  cordial  assistance  and  support 
rendered  by  a  number  of  the  author's  friends  and  col- 
leagues, who  have  supplied  him  with  the  material  ne- 
cessary to  the  presentation  of  their  latest  researches. 
Professor  Campbell  has  supplied  nearly  all  the  ma- 
terial relating  to  spectroscopic  binary  systems,  com- 
pleted and  revised  the  list  of  those  objects,  and  freely 
placed  at  the  author's  disposal  photographs  taken  at 
the  Lick  Observatory,  including  the  frontispiece  to 
the  volume.  Professor  Kapteyn  has  supplied  a  large 
mass  of  material,  published  and  unpublished,  relating 
to  his  researches  in  stellar  statistics,  of  which,  how- 
ever, only  inadequate  use  could  be  made.  Professor 
Pickering  has  permitted  the  free  use  of  the  treasures 
contained  in  the  circulars  and  other  publications  of 
the  Harvard  Observatory,  and  Sir  William  Huggins 
has  communicated  the  results  of  his  latest  studies  in 
the  life-history  of  the  stars.  Drs.  A.  A.  Common  and 
Isaac  Roberts  have  each  supplied  a  specimen  of 
their  photographs  o  and  Father  Sidgreaves, 


PREFACE 


S.  J.,  of  his  photographs  of  spectra  taken  at  the 
Stonyhurst  College  Observatory.  Professor  Barnard 
has  allowed  the  use  of  his  photographs  of  the  Milky 
Way. 


CONTENTS. 

CHAPTER  I. 
REVIEW  OF  RECENT  PROGRESS. 

PACK 

Extension  of  Research  into  the  Southern  Hemisphere  —  The  Revelations 

of  the  Spectroscope  —  The  Lick  and  Harvard  Observatories      .        .         i 

CHAPTER  II. 
MAGNITUDES  OF  THE  STARS. 

The  Brightness  of  a  Star  Depends  on  Distance — Ancient  System  of  Mag- 
nitudes —  Modern  Conception  of  Magnitude  — -  Effect  of  Color  on 
Magnitude  —  Photographic  Magnitudes — Photometric  Surveys  of  the 
Heavens — Stellar  Magnitude  of  the  Sun 15 


CHAPTER  III. 

CONSTELLATIONS  AND  STAR  NAMES. 

Study  of  the  Constellations — The  Uronometria  Argentina — Naming  the 

Stars — Relation  of  Names  to  Constellations 2$ 

CHAPTER  IV. 
CATALOGUING  AND  NUMBERING  THE  STARS. 

Right  Ascension  and  Declination  —  Ancient  and  Mediaeval  Catalogues  of 
Stars — Modern  Catalogues — Durchmusterung  of  Argelander  SchOn- 
feld,  Thome,  Gill,  and  Kapteyn— Numbering  the  Stars  ...  38 


viii  CONTENTS 

CHAPTER  V. 
THE  SPECTRA  OF  THE  STARS. 

PAGE 

Principles  of  Spectrum  Analysis — Description  of  the  Visible  Spectrum — 
Special  Lines  and  Wave-Lengths  —  Classification  of  Stellar  Spectra 
— General  Results  of  Spectrum  Analysis 56 

CHAPTER  VI. 
PROPER  MOTIONS  OF  THE  STARS. 

Apparent  and  Real  Motions — Swiftness  of  the  Motions — Stars  of  Large 
Proper  Motion — Moving  Systems  of  Stars — Radial  Motions  of  the 
Stars — The  Motion  of  the  Sun — Position  of  the  Solar  Apex — Speed 
of  the  Solar  Motion 75 

CHAPTER  VII. 
VARIABLE  STARS. 

Periodic  Stars— Light  Curve  of  a  Star— The  Omicron  Ceti  Type— The 
Algol  Type  — The  Beta  Lyrse  Type  —  Combination  of  the  Two 
Types — Variations  of  Eta  Aquilse — Classification  of  Variable  Stars 
— Possible  Secular  Variations  of  the  Brillancy  of  Stars  —  Spectra  of 
Variable  Stars  . 94 

CHAPTER  VIII. 

NEW  STARS. 

Eta  Argus— List  of  New  Stars— Tycho's  Star  of  1752— Kepler's  Star  of 

1604— T  Corona — Nova  Aurigae — Nova  Persei 123 


CHAPTER  IX. 
THE  PARALLAXES  OF  THE  STARS. 

Early  Attempts  to  Measure  Parallax  —  First  Measures  of  Parallax  — 
Modern  Methods  — The  Heliometer  and  Photographic  Telescope- 
Surveys  for  Parallax  .........  140 


CONTENTS  ix 

CHAPTER  X. 
SYSTEMS  OF  STARS. 

PACK 

Double  Stars — Position,  Angle,  and  Distance — Orbits  of  Double  Stars — 
Binary  Systems  of  Sirius  and  Procyon  —  Orbit  of  Alpha  Centauri — 
System  of  Capella  —  Triple  and  Multiple  Systems  —  Spectroscopic 
Binary  Systems — Star-Clusters — Variable  Stars  in  Clusters  .  .  153 

CHAPTER  XI. 

NEBULAE. 

Great  Nebula  of  Orion  — Other   Remarkable   Nebulae  —  Discovery  of 

Nebulae  by  Photography— Physical  Constitution  of  the  Nebulae        .     178 

CHAPTER  XII. 
CONSTITUTION  OF  THE  STARS. 

Masses  and  Densities  of  the  Stars — Diversities  among  the  Stars — Masses 
and  Densities  of  the  Binary  Systems  —  Gaseous  Constitution  of  the 
Stars 191 

CHAPTER  XIII. 

STELLAR  EVOLUTION. 

Life  History  of  a  Star— Changes  in  the  Spectra 217 

CHAPTER  XIV. 
THE  STRUCTURE  OF  THE  HEAVENS. 

Is  the  Universe  Finite  ? — Arrangement  of  the  Stars  in  Space — Relation  of 
the  Milky  Way  to  the  Universe  —  Possible  Hypotheses  as  to  the 
Arrangement  of  the  Stars 226 

CHAPTER  XV. 
APPARENT  DISTRIBUTION  OF  THE  STARS  IN  THE  SKY. 

Distribution  of  the  Lucid  Stars — Distribution  of  the  Fainter  Stars — Dis- 
tribution of  the  Stars  having  Sensible  Proper  Motions — Distribution 
of  Fifth  Type 238 


x  CONTENTS 

CHAPTER  XVI. 

THE  CLUSTERING  OF  THE  STARS. 

PAGE 

The  Pleiades  —  Coma  Berenices  —  Prsesepe  —  Orion  .        *  258 

CHAPTER  XVII. 

THE  STRUCTURE  OF  THE  MILKY  WAY. 

Description  of  the  Milky  Way  — Lucid  Stars  belonging  to  the  Milky 
Way  — Fainter  Stars  belonging  to  the  Milky  Way  — Rifts  in  the 
Milky  Way .264 

CHAPTER  XVIII. 

THE  PROGRESSION  IN  THE  NUMBER  OF  STARS  AS  THE 
BRIGHTNESS  DIMINISHES. 

Ratio  of  this  Increase  in  Different  Regions  of  the  Sky  —  Higher  ratio  in 

the  galaxy 27? 


CHAPTER  XIX. 

STATISTICAL  STUDIES  OF  PROPER  MOTIONS. 

Components  of  the  Proper  Motion  —  Mean  Parallax  of  the  Stars  of  the 
Second  Magnitude  —  Motions  of  the  Two  Principal  Spectral  Types 
of  Stars — Kapteyn's  Researches — Relation  of  the  Proper  Motions  to 
the  Solar  Motion  .  286 


CHAPTER  XX. 
THE  DISTRIBUTION  OF  THE  STARS  IN  SPACE. 

Number  of  Stars  at  Different  Distances— Probable  Thickness  of  the  Stars 
in  Space— Mean  Parallaxes  of  the  Stars— Possible  Distance  of  the 
Milky  Way 305 


ILLUSTRATIONS 

PAGB 

THE  TRIPHID  NEBULA Frontispiece 

LAW  OF  CHANGE  OF  THE  MAGNITUDE  OF  A  STAR  WITH  ITS  DISTANCE  .  15 

PLAN  OF  THE  SPECTRUM         ; 65 

EXAMPLES  OF  STELLAR  SPECTRA 68 

SPECTROGRAM  OF    POLARIS    TAKEN    BY    CAMPBELL   AT   THE   LICK 

OBSERVATORY 84 

THE  MILLS  SPECTROGRAPH  OF  THE  LICK  OBSERVATORY        ...  86 

LIGHT-CURVE  OF  A  VARIABLE  STAR 98 

FORM  OF  LIGHT-CURVE  OF  AN  ALGOL  VARIABLE 102 

LIGHT-CURVE  OF  U  PEGASI .in 

LIGHT- AND  VELOCITY-CURVES  OF  77  AQUIL^ 114 

SPECTRUM  OF  o  CETI  NEAR  MAXIMUM  OF  1897 120 

SPECTRUM  OF  NOVA  AURIGA 133 

DISTANCE  AND  POSITION-ANGLE  OF  A  DOUBLE  STAR      .        •        .        .  155 

APPARENT  ORBIT  OF  a  CENTAURI  ........  162 

RADIAL  MOTION  OF  A  BINARY  SYSTEM 166 

THE  GREAT  STAR-CLUSTER  OF  HERCULES      ...,,.  171 

THE  GREAT  STAR-CLUSTER  OF  GO  CENTAURI .  175 

THE  GREAT  NEBULA  OF  ORION 180 

THE  GREAT  SPIRAL  NEBULA  M.  51 181 

THE  GREAT  NEBULA  OF  ANDROMEDA     .......  182 

NEBULOUS  MASS  IN  CYGNUS 186 

Two  BINARY  SYSTEMS  ON  THE  SAME  MODEL 196 

POSSIBLE  SECTIONS  OF  THE  GALAXY 235 

SCHIAPARELLI'S   PLANISPHERES    SHOWING   THE   RICHNESS  OF  THE  SKY 

IN  LUCID  STARS 244,  245 

PHOTOGRAPH  SHOWING  STRUCTURE  OF  THE  MILKY  WAY      .        .        .270 

RIFTS  IN  THE  MILKY  WAY 272 

COMPONENTS  OF  PROPER  MOTION 294 

xi 


THE  STARS 


CHAPTER  I 

REVIEW  OF  RECENT  PROGRESS 

These  are  thy  glorious  works,  Parent  of  good, 
Almighty,  thine  this  universal  frame, 
Thus  wondrous  fair. — MILTON. 

WE  begin  our-  study  of  the  stars  by  a  glance  at  the 
structure  of  the  universe.  What  are  familiarly 
known  as  the  heavenly  bodies  belong  to  two  classes 
which  are  very  different  as  regards  their  relation  to 
our  earth.  Those  nearest  to  us  form  a  sort  of  colony 
far  removed  from  all  the  others,  called  the  solar  sys- 
tem. The  principal  bodies  of  this  system  are  the 
sun  and  eight  great  planets,  with  their  moons,  re- 
volving round  it.  On  one  of  these  planets,  small 
when  compared  with  the  great  bodies  of  the  universe, 
but  large  to  our  every-day  conceptions,  we  dwell.  The 
other  planets  appear  to  us  as  stars.  Four  of  them, 
Venus,  Mars,  Jupiter,  and  Saturn,  are  distinguished 
from  the  fixed  stars  by  their  superior  brightness  and 


z  REVIEW  OF  RECENT  PROGRESS 

characteristic  motions.  Of  the  remaining  three,  Mer- 
cury will  rarely  excite  notice,  while  Uranus  is  nearly 
invisible  to  the  naked  eye,  and  Neptune  quite  so. 

The  dimensions  of  the  solar  system  are  vast  when 
compared  with  any  terrestrial  standard.  A  cannon- 
shot  going  incessantly  at  its  usual  speed  would  be  five 
hundred  years  in  crossing  the  orbit  of  Neptune  from 
side  to  side.  But  vast  as  these  dimensions  are,  they 
sink  into  insignificance  when  compared  with  the  dis- 
tances of  the  stars.  Outside  the  solar  system  are 
spaces  which,  so  far  as  we  know,  are  absolutely  void, 
save  here  and  there  a  comet  or  a  meteor,  until  we  look 
far  outside  the  region  which  a  cannon-shot  would  cross 
in  a  million  of  years.  The  nearest  star  is  thousands 
of  times  farther  away  than  the  most  distant  planet. 
Scattered  at  these  inconceivable  distances  are  the 
bodies  to  which  our  attention  is  directed  in  the  present 
work.  If  we  are  asked  what  they  are,  we  may  reply 
that  the  stars  are  suns.  But  we  might  equally  well 
say  that  the  sun  is  one  of  the  stars ;  a  small  star, 
indeed,  surrounded  by  countless  others,  many  of 
which  are  much  larger  and  brighter  than  itself.  We 
shall  treat  our  theme  as  far  as  possible  by  what  we  may 
call  the  natural  method,  beginning  with  what,  being 
most  obvious  to  the  eye,  was  first  noticed  by  man,  or 
will  be  first  noticed  by  an  observer,  and  tracing  know- 
ledge up  step  by  step  to  its  present  state. 

Several  features  of  the  universe  of  stars  will  be  evid- 
ent at  a  glance.  One  of  these  is  the  diversity  of  the 
apparent  brightness,  or,  in  technical  language,  of  the 
magnitudes  of  the  stars.  A  few  far  outshine  the  great 


REVIEW  OF  RECENT  PROGRESS.  3 

mass  of  their  companions.  A  greater  number  are  of 
what  we  may  call  medium  brightness  ;  there  is  a  yet 
larger  number  of  fainter  ones,  and  about  one-half  of  all 
those  seen  by  a  keen  eye  under  favourable  conditions 
are  so  near  the  limit  of  visibility  as  to  escape  ordinary 
notice.  Moreover,  those  which  we  see  are  but  an  in- 
significant fraction  of  the  number  revealed  by  the 
telescope.  The  more  we  increase  our  optical  power, 
the  greater  the  number  that  come  into  view.  How 
many  millions  may  exist  in  the  heavens  it  is  scarcely 
possible  even  to  guess.  The  photographic  maps  of 
the  heavens  now  being  made  probably  show  more  than 
fifty  millions,  perhaps  one  hundred  millions,  possibly 
twice  this  number. 

Another  evident  feature  is  the  tendency  of  the 
brighter  stars  to  cluster  into  groups,  known  as  con- 
stellations. The  latter  are  extremely  irregular,  so  that 
we  cannot  always  decide  where  one  constellation 
should  end  and  another  begin,  or  to  which  constella- 
tion a  certain  star  may  belong.  Hence,  the  definition 
and  mapping  out  of  the  constellations  and  the  division 
of  the  stars  among  them  are  somewhat  arbitrary 
proceedings. 

A  third  feature  is  the  Milky  Way  or  Galaxy,  which 
to  ordinary  vision  appears  as  an  irregular  succession 
of  cloud-like  forms  spanning  the  heavens.  We  now 
know  that  these  seeming  clouds  are  really  congeries 
of  stars  too  faint  to  be  individually  visible  to  the  na- 
ked eye.  We  shall  hereafter  see  that  the  stars  of  the 
Galaxy  form,  so  to  speak,  the  base  on  which  the  uni- 
verse appears  to  be  constructed. 


4  RE  VIE  W  OF  RECEN  T  PROGRESS 

Each  of  these  three  features  will  be  considered  in 
its  proper  place.  In  the  present  chapter  we  shall 
make  a  rapid  survey  of  what  has  been  done  in  our 
time  to  advance  our  knowledge  of  the  stars. 

A  natural  result  of  the  northern  hemisphere  being 
the  home  of  civilised  peoples  was  that,  until  recent 
times,  the  study  of  the  southern  heavens  had  been 
comparatively  neglected.  It  is  true  that  the  curiosity 
of  the  enquiring  astronomers  of  the  past  would  not  be 
satisfied  without  their  knowing  something  of  what  was 
to  be  seen  south  of  the  equator.  Various  enterprises 
and  establishments  had  therefore  contributed  to  our 
knowledge  of  the  region  in  question.  As  far  back  as 
1677,  during  a  voyage  to  St.  Helena,  Halley  cata- 
logued the  brighter  stars  in  the  region  near  the  South 
Pole.  About  1750  Lacaille,  of  France,  established  an 
observing  station  at  the  Cape  of  Good  Hope,  and 
made  a  catalogue  of  several  thousand  stars,  which  has 
remained  a  handy-book  for  the  astronomer  up  to  the 
present  time.  In  1834-38  Sir  John  Herschel  made  a 
special  voyage  to  the  Cape  of  Good  Hope,  armed  with 
the  best  telescopes  which  his  father  had  shown  him 
how  %to  construct,  for  the  purpose  of  doing  for  the 
southern  heavens  as  much  as  possible  of  what  his 
father  had  done  for  the  northern.  The  work  of  this 
expedition  forms  one  of  the  most  important  and  inter- 
esting chapters  in  the  history  of  astronomic  science. 
Not  only  is  Herschel's  magnificent  volume  a  classic 
of  astronomy,  but  the  observations  which  it  contains 
are  still  as  carefully  and  profitably  studied  as  any  that 
have  since  been  made.  They  may  be  said  to  form 


REVIEW  OF  RECENT  PROGRESS  5 

the  basis  of  our  present  knowledge  of  the  region  which 
they  included  in  their  scope. 

Herschel's  work  may  be  described  as  principally  in 
the  nature  of  an  exploration.  He  had  no  instruments 
for  accurately  determining  the  positions  of  stars.  In 
the  latter  field  the  first  important  contributions  after 
Lacaille  were  made  by  Sir  Thomas  Brisbane,  Gov- 
ernor of  New  South  Wales,  and  Rumker,  his  assist^ 
ant,  at  Paramatta.  Johnson,  of  England,  about  1830, 
introduced  modern  accuracy  into  the  Construction  of  a 
ratherlimitedcatalogue  of  stars  which  he  observed  atSt. 
Helena.  About  the  same  time  the  British  Government 
established  the  observatory  at  the  Cape  of  Good  Hope, 
which  has  maintained  its  activity  to  the  present  time. 
About  the  middle  of  the  century  the  Government  of 
New  South  Wales  established,  first  at  Williamstown 
and  then  at  Melbourne,  an  observatory  which  has 
worked  in  the  same  field  with  marked  success. 

An  American  enterprise  in  the  same  direction  was 
that  of  Captain  James  M.  Gilliss,  who,  in  1849, 
organised  an  astronomical  expedition  to  Chili.  The 
principal  motive  of  this  enterprise  was  the  determina- 
tion of  the  solar  parallax  by  observations  upon  Venus 
and  Mars  about  the  time  of  their  nearest  approach  to 
the  earth.  As  these  observations  would  take  but  a 
small  part  of  his  time,  Gilliss  determined  to  take  with 
him  instruments  for  determining  the  positions  of  the 
stars.  He  established  his  observatory  at  a  point  near 
Santiago,  where  he  continued  his  observations  for 
nearly  three  years.  He  was  an  excellent  practical 
observer,  but  an  untoward  circumstance  detracted 


6  REVIEW  OF  RECENT  PROGRESS 

from  the  value  of  his  work.  His  observatory  was 
built  upon  a  rocky  eminence,  a  foundation  which 
seemed  to  afford  the  best  possible  guaranty  of  the 
stability  of  his  instruments.  He  made  no  attempt  to 
reduce  his  observations  till  after  his  return  home. 
Then  it  was  found  that  the  foundation,  through  the 
expansion  and  contraction  due  to  the  heat  of  the  sun, 
was  subject  to  a  diurnal  change  which  made  it  ex- 
tremely difficult  to  derive  good  results  from  his  care- 
ful work.  It  was  not  until  1896,  more  than  thirty 
years  after  his  death,  that  the  catalogue  of  the  stars 
observed  by  him  was  at  last  completed  and  published. 

We  do  not  derogate  in  any  way  from  the  merit  of 
these  efforts  in  saying  that  they  could  not  lead  to 
results  comparable  with  those  of  the  score  of  richly 
equipped  northern  observatories  which  the  leading  na- 
tions and  universities  of  Europe  had  endowed  and  sup- 
ported for  more  than  a  hundred  years.  Only  within 
the  last  thirty  years  has  it  been  possible  to  bring  our 
knowledge  of  the  southern  heavens  up  to  a  satisfac- 
tory stage.  Now,  however,  the  progress  of  southern 
astronomy,  if  we  may  use  the  term,  is  such  that  in 
several  points  our  knowledge  of  the  southern  heavens 
surpasses  that  of  the  northern  ones.  If  we  measure 
institutions  by  the  importance  of  the  work  they  are 
doing,  there  are  several  in  the  southern  hemisphere 
which  must  to-day  be  placed  in  the  first  rank. 

The  history  and  work  of  the  Cordoba  Observatory 
are  of  special  interest.  In  1870  Dr.  B.  A.  Gould, 
who  might  fairly  be  considered  as  the  father  of 
modern  American  astronomy,  conceived  the  idea  of 


REVIEW  OF  RECENT  PROGRESS  ^ 

•establishing  an  observatory  of  the  first  class  in  South 
America.  He  found  the  President  and  Government 
of  the  Argentine  Republic  ready  to  support  his 
scheme  with  a  liberality  well  fitted  to  impress  us  with 
a  high  sense  of  their  standard  of  civilisation.  In  a 
year  or  two  the  observatory  at  Cordoba  was  in  active 
operation.  The  discussions  to  which  its  work  gives 
rise  belong  to  a  subsequent  chapter.  But  there  is 
one  branch  that  is  worthy  of  special  mention  in  the 
present  connection.  The  Uranometria  Argentina, 
published  in  1879,  m  a  quarto  volume,  with  a  large 
atlas,  must  be  regarded  as  one  of  the  most  remark- 
able contributions  yet  made  to  our  knowledge  of  the 
southern  sky.  It  is  concerned  exclusively  with  the 
objects  visible  to  the  naked  eye,  or  at  most  with  an 
opera-glass.  These  were  studied,  described,  cata- 
logued, and  mapped  with  a  minuteness  of  detail 
exceeding  anything  yet  done  in  that  line  for  the  north- 
ern sky.  The  notes  to  the  catalogue  alone  comprise 
fifty  pages,  but  being  duplicated  in  the  English  and 
Spanish  languages,  really  fill  more  than  a  hundred. 
A  particular  watch  was  kept  up  for  variable  stars  ; 
and  the  evidence,  conclusive  or  doubtful,  for  varia- 
bility, takes  up  an  important  part  of  the  notes.  These 
are  followed  by  a  discussion  of  the  distribution  of  the 
stars,  primarily  of  the  southern  hemisphere,  but  in- 
cidentally including  the  northern,  which  must  still  be 
regarded  as  a  standard  study  of  the  subject.  Dr. 
Gould  continued  in  active  charge  of  the  Cordoba 
Observatory  until  1885,  when  he  returned  home,  and 
was  succeeded  by  Thome,  the  present  director. 


8  REVIEW  OF  RECENT  PROGRESS 

A  few  years  after  Gould  went  to  Cordoba,  Gill  was 
made  director  of  the  Royal  Observatory  at  the  Cape 
of  Good  Hope.  The  rapid  growth  of  this  institution 
to  one  of  the  first  rank  is  due  no  less  to  the  scientific 
ability  of  the  new  director  than  to  the  unflagging 
energy  which  he  has  devoted  to  the  enlargement  of 
the  resources  of  the  institution.  The  great  fact  which 
he  sought  to  impress  upon  his  supporters  was  that 
the  southern  celestial  hemisphere  was  as  large  as  the 
northern,  and  therefore  equally  worthy  of  study. 

In  any  general  review  of  the  progress  of  stellar  as- 
tronomy during  the  past  twenty  years,  we  should  find 
the  Harvard  Observatory  before  us  at  every  turn. 
What  it  has  done  will  be  seen,  though  in  an  imperfect 
way,  in  subsequent  chapters.  Not  satisfied  with  the 
northern  hemisphere,  it  has  established  a  branch  at 
Arequipa,  Peru,  in  which  its  methods  of  observation 
and  research  are  extended  to  the  south  celestial  pole. 
Its  principal  specialty  has  been  the  continuous  ex- 
ploration of  the  heavens.  Celestial  photography, 
photometry,  and  spectroscopy  sum  up  its  fields  of 
activity.  For  more  than  ten  years  it  might  be  almost 
said  that  a  sleepless  watch  of  the  heavens  has  been 
kept  up  by  an  all-seeing  photographic  eye,  with  an 
accuracy  of  which  the  world  has  hardly  had  a  concep- 
tion. The  completeness  with  which  its  work  has  been 
done  has  recently  been  shown  in  a  striking  way. 

Our  readers  are  doubtless  acquainted  with  the 
singular  character  of  the  minor  planet  Eros,  whose 
orbit  passes  through  that  of  Mars,  as  one  link  of  a 
chain  passes  through  another,  and  which  comes  nearer 


THE  SPECTROSCOPE  9 

the  earth  at  certain  times  than  any  other  celestial 
body,  the  moon  excepted.  When  the  character  of 
the  orbit  became  established,  it  was  of  interest  to 
know  whether  the  planet  had  ever  been  observed  as 
a  fixed  star  at  former  oppositions.  Chandler,  having 
computed  the  path  of  the  planet  at  the  most  import- 
ant of  the  oppositions,  beginning  with  1892-94,  com- 
municated his  results  to  Director  Pickering,  and 
suggested  a  search  of  the  Harvard  photographs  to 
see  if  the  planet  could  be  found  on  them.  The  result 
was  the  discovery  of  the  planet  upon  more  than  a 
score  of  plates  taken  at  various  times  during  the  pre- 
ceding ten  years. 

New  stars  were  formerly  supposed  to  be  of  very 
rare  occurrence,  but  since  the  Harvard  system  of 
photographing  the  heavens  has  been  introduced,  five 
or  six  have  been  known  to  burst  forth. 

Although  the  first  application  of  the  spectroscope 
to  the  study  of  the  heavenly  bodies  was  made  within 
the  memory  of  the  present  generation,  its 

111  11  i  i  •  The  Spec- 

results  have  been  only  less  epoch-making        troscope 

than  those  of  the  telescope.  The  two  in-  and  Photo- 
struments  differ  in  that  the  one,  bringing 
all  the  light  from  a  star  which  falls  on  its 
object-glass  to  one  focus,  sends  it  all  into  the  eye, 
thus  multiplying  it  hundreds  or  thousands  of  times, 
and  bringing  into  view  a  universe  of  stars  formerly  in- 
visible. The  newer  instrument  operates  by  analysing 
the  light  collected  by  the  telescope  into  its  separate 
colors  or  kinds,  which  it  arranges,  as  it  were,  on  a 
sheet.  The  sheet  is  simply  the  retina  of  the  eye  on 


io  RE 'VIE 'IV  OF  RECENT  PROGRESS 

which  the  spectrum  is  formed.  Thus  the  eye  is  en- 
abled to  see  the  quantity  of  light  on  every  part  of  the 
sheet,  and  by  the  immense  variety  of  arrangement 
which  the  method  admits  of,  remarkable  conclusions 
respecting  the  constitution  and  motion  of  the  body 
that  emits  the  light  can  be  drawn.  The  most  dis- 
tinctive feature  of  the  spectroscopic  method  arises 
from  the  fact  that  the  composition  of  the  light  is  in- 
dependent of  the  distance  of  the  body.  The  spec- 
troscopist  can  therefore  draw  conclusions  as  to  the 
constitution  and  motion  of  the  most  distant  star,  as 
readily  as  he  can  about  those  of  the  flame  within  his 
laboratory. 

Spectroscopy  has,  in  recent  times,  been  re-enforced 
by  photography.  In  the  early  '40*5,  Dr.  Draper  took 
a  daguerreotype  of  the  moon.  As  the  photographic 
art  was  developed,  astronomers  naturally  occupied 
themselves  with  photographing  celestial  bodies  by  the 
light  which  they  emitted.  For  this  purpose  the  tele- 
scope could  be  used  as  a  camera.  The  first  important 
step  in  this  direction  was  taken  by  Bond  at  Harvard. 
The  next  great  advance  was  made  by  Rutherfurd  of 
New  York,  who  photographed  clusters  of  stars  and 
used  the  plates  in  determining  the  positions  of  the 
individual  bodies  of  the  cluster. 

When  more  sensitive  chemicals  were  introduced 
into  photography,  another  step  in  advance  was  made 
by  combining  the  spectroscopic  and  the  sensitive 
plate  into  a  spectrograph.  In  all  the  more  serious 
spectroscopic  work  of  the  present  day  the  spectrum  is 
photographed,  and  the  astronomer,  or  astrophysicist 


THE  SPECTROSCOPE  AND  PHOTOGRAPHY    ir 

as  he  now  calls  himself,  can  study  and  measure  the 
plates  at  his  leisure. 

The  great  revelations  of  our  times  have  come 
through  the  application  of  this  method  to  the  meas- 
urement of  motions  in  the  line  of  sight  from  us  to  a 
star.  No  achievement  of  the  intellect  of  man  would 
have  seemed  farther  without  the  range  of  possibility 
to  the  thinker  of  half  a  century  ago  than  the  dis- 
coveries of  invisible  bodies  which  are  now  being  made 
by  such  measurements.  The  revelations  of  the  tele- 
scope take  us  by  surprise.  But  if  we  consider  what 
the  thinker  alluded  to  might  regard  as  attainable,  they 
are  far  surpassed  by  those  of  the  spectroscope.  The 
dark  bodies,  planets  we  may  call  them,  which  are  re- 
volving round  the  stars,  must  be  for  ever  invisible  in 
any  telescope  that  it  would  be  possible  to  construct. 
They  would  remain  invisible  if  the  power  of  the  in- 
strument were  increased  ten  thousand  times.  And 
yet  if  there  are  inhabitants  on  these  planets,  our  as- 
tronomers could  tell  them  more  of  the  motions  of  the 
world  on  which  they  live  than  the  human  race  knew 
of  the  motions  of  the  earth  before  the  time  of 
Copernicus. 

The  men  and  institutions  which  have  contributed 
to  this  result  are  so  few  in  number  that  it  will  not  be 
tedious  to  mention  at  least  the  principal  actors.  The 
possibility  of  measuring  the  motions  of  the  stars  in 
the  line  of  sight  by  means  of  the  spectroscope  was 
first  pointed  out  by  Mr  now  Sir  William  Huggins. 
He  actually  put  the  method  into  operation.  As  soon 
as  its  feasibility  was  demonstrated  it  was  taken  up  at 


12  REVIEW  OF  RECENT  PROGRESS 

Greenwich.  In  these  earlier  attempts,  eye  methods 
alone  were  used,  and  the  results  were  not  always  re- 
liable. Then  spectrum  photography  was  applied  at 
the  German  astrophysical  observatory  of  Potsdam  by 
Vogel,  who  introduced  into  the  method  a  degree  of 
precision  which  had  never  before  been  reached.  His 
measures  of  the  motions  of  the  stars  in  the  line  of  sight 
opened  up  the  last  era  in  science.  Applying  the 
method  to  the  variable  star  Algol,  he  proved  that  the 
loss  of  light  which  it  undergoes  at  intervals  of  nearly 
three  days  is  merely  a  partial  eclipse  by  a  dark  planet, 
almost  as  large  as  itself,  revolving  round  it.  Thus  was 
discovered  a  new  order  of  bodies  in  the  universe, 
telescopic  binary  systems,  pairs  of  stars,  or  stars  and 
planets,  revolving  round  each  other  by  their  mutual 
gravitation  ;  although  no  telescope  that  it  is  possible 
to  make  would  ever  show  that  more  than  a  single 
body  was  present.  Thence  the  photographic  method 
soon  spread  to  Meudon  and  Pulkova.  But,  as  often 
happens  when  new  fields  of  research  are  opened,  we 
find  them  cultivated  in  quarters  where  we  should  least 
expect.  The  successful  application  of  the  method  re- 
quires not  only  the  best  spectroscope,  but  the  most 
powerful  telescope  at  command.  Ten  years  ago  the 
most  powerful  telescope  in  the  world  was  at  the  Lick 
Observatory.  A  few  years  later  Mr.  D.  O.  Mills  put 
at  its  eye  end  the  best  spectrograph  that  human  art 
could  make  at  that  time,  the  work  of  Brashear.  It  is 
Campbell  who,  with  this  instrument,  has  inaugurated 
a  series  of  discoveries  in  this  line  which  are  without 
a  parallel.  He  finds  that  about  one  star  in  thirteen 


THE  SPECTROSCOPE  AND  PHOTOGRAPHY    13 

has  a  planet  revolving  round  it,  so  massive  as  to 
change  the  motion  of  the  star  by  an  amount  visible 
in  the  spectroscope.  The  more  or  less  eccentric 
orbits  of  these  bodies  are  being  determined.  The 
final  conclusion  from  all  his  work  is  that  isolated  stars 
may  be  the  exception  rather  than  the  rule ;  that  pos- 
sibly a  great  majority  at  least  of  the  stars  are  composed 
of  two  or  more  bodies  revolving  round  each  other, 
though  they  appear  in  our  telescopes  as  single. 

The  study  of  variable  stars  from  being  little  more 
than  a  scientific  amusement,  has  grown  into  an  im- 
portant branch  of  astronomical  science.  It  has  now 
joined  hands  with  spectroscopy  to  make  it  probable 
that  in  most  cases  the  variations  of  light  in  a  star  are 
due  to  changes  in  its  constitution  produced  by  in- 
visible planets  revolving  round  it. 

All  these  results  naturally  involve  a  great  increase 
in  the  number  of  men  who  are  devoting  themselves 
to  astronomical  research.  When  we  study  the  work 
of  this  small  army  of  investigators,  and  compare  the 
possibilities  of  the  field  they  are  exploring  with  what 
has  been  done  in  the  past,  we  feel  that  astronomy, 
although  the  oldest  of  the  sciences  in  years,  is  reach- 
ing a  stage  of  vigorous  youth,  and  that  the  twentieth 
century  will  open  up  views  of  the  universe  of  which 
quite  possibly  we,  at  its  beginning,  have  no  conception. 

A  mere  survey  of  what  has  been  done  in  the  vari- 
ous lines  we  have  mentioned  would  be  far  from  giving 
an  idea  of  the  real  significance  of  the  advance  we  are 
considering.  Cataloguing  the  stars,  estimating  their 
magnitudes,  recording  and  comparing  their  spectra, 


i4  REVIEW  OF  RECENT  PROGRESS 

and  determining  their  motions  might  be  considered 
as,  after  all,  barren  of  results  of  the  highest  human 
interest.  When  we  know  the  exact  position  of  every 
star  in  the  heavens,  the  direction  in  which  it  is  mov- 
ing, and  the  character  of  its  spectral  lines,  how  much 
wiser  are  we  ? 

What  could  hardly  have  been  foreseen  fifty  years 
ago,  is  that  these  various  classes  of  results  are  now 
made  to  combine  and  converge  upon  the  greatest 
problem  which  the  mind  of  man  has  ever  attempted 
to  grasp — that  of  the  structure  of  the  universe.  The 
study  of  variable  stars  has  suddenly  fallen  into  line, 
so  to  speak,  so  that  now  it  is  uniting  itself  to  the 
study  of  all  the  other  celestial  objects,  to  give  us  at 
least  a  faint  conception  of  what  the  solution  of  this 
problem  may  be. 

One  of  the  principal  objects  of  the  present  work  is 
to  make  a  comparison  of  these  various  researches, 
and  discuss  the  views  respecting  the  constitution  of 
the  stars  individually,  as  well  as  of  the  universe  as 
a  whole,  to  which  they  lead  us.  But  there  are  a 
number  of  details  to  be  considered  singly  before  we 
can  combine  results  in  this  way.  Our  early  chapters 
will,  therefore,  be  devoted  to  the  special  features  and 
individual  problems  of  stellar  astronomy  which  have 
occupied  the  minds  of  astronomers  from  the  begin- 
ning of  their  work  to  the  present  time.  Keeping 
these  details  in  mind,  we  can  profitably  proceed  to  the 
consideration  of  the  general  conclusions  to  be  drawn 
from  them. 


CHAPTER  II 

MAGNITUDES  OF  THE  STARS 

And  one  star  differeth  from  another  star  in  glory. — PAUL. 

THE  apparent  brightness  of  a  star,  as  we  see  it  from 
the  earth,  depends  upon  two  causes  —  its  intrin- 
sic brilliancy,  or  the  quantity  of  light  which  it  actually 
emits,  and  its  distance  from  us.  It  follows  that  if  all 
the  stars  were  of  equal  intrinsic  brightness  we  could 
determine  their  relative  distances  by  measuring  the  re- 
spective amounts  of  light  which  we  receive  from  them. 
The  quantity  of  light  in  such  a  case  varies  inversely 
as  the  square  of  the  distance.  This  will  be  seen  by 
the  figure,  where  S  represents  the  position  of  a  star, 


regarded  as  a  luminous  point,  while  A  and  B  B  B  B  are 
screens  placed  at  such  distances  that  each  will  re- 
ceive the  same  amount  of  light  from  the  star.  If  the 


1 6  MAGNITUDES  OF  THE  STARS 

larger  screen  is  twice  as  far  as  the  screen  A,  its  sides 
must  be  twice  as  long  in  order  that  it  shall  receive 
all  the  light  that  would  fall  on  A.  In  this  case,  its 
surface  will  be  four  times  the  surface  of  A.  It  is 
then  evident  that  each  quarter  of  the  surface 
marked  B  will  receive  one-fourth  as  much  light  as 
the  surface  A.  Thus,  an  eye  or  a  telescope  in  the 
position  B  will  receive  from  the  star  one-fourth  as 
much  light  as  in  the  position  A,  and  the  star  will 
seem  one-fourth  as  bright. 

The  fact  is,  however,  that  the  stars  are  very  un- 
equal in  their  actual  brightness,  and  in  consequence 
the  apparent  magnitude  of  a  star  gives  us  no  clue 
to  its  distance.  Among  the  nearer  of  the  stars  are 
some  scarcely,  if  at  all,  visible  to  the  naked  eye, 
while  among  the  brighter  ones  are  several  whose 
distances  are  immeasurably  great.  A  remarkable  ex- 
ample is  that  of  Canopus,  the  second  brightest  star 
in  the  heavens. 

For  these  reasons  astronomers  are  obliged  to  con- 
tent themselves,  in  the  first  place,  with  determina- 
tions of  the  actual  amount  of  light  that  the  various 
stars  send  to  us,  or  their  apparent  brilliancy,  without 
regard  to  their  distance  or  actual  brilliancy.  The 
ancient  astronomers  divided  all  the  stars  they  could 
see  into  six  classes,  the  number  expressing  the  appar- 
ent brightness  being  called  the  magnitude  of  the  star. 
The  brightest  ones,  numbering  in  all  about  fourteen, 
were  said  to  be  of  the  first  magnitude.  The  fifty 
next  in  brightness  were  said  to  be  of  the  second  mag- 
nitude. Three  times  as  many,  an  order  fainter,  were 


MAGNITUDES  OF  THE  STARS  17 

of  the  third  magnitude.  The  progression  was  con- 
tinued up  to  the  sixth  magnitude,  which  included 
those  which  were  barely  visible. 

As  the  stars  are  actually  of  every  degree  of  appar- 
ent brilliancy,  no  sharp  line  of  demarkation  could  be 
drawn  between  those  of  one  magnitude  and  those 
of  the  magnitude  next  higher.  Hence,  different  ob- 
servers made  different  estimates,  some  calling  a  star 
of  the  second  magnitude  which  others  would  call  of 
the  first,  and  designating  as  of  the  third  magnitude  one 
which  others  would  call  of  the  second.  It  is  there- 
fore impossible  to  state,  with  absolute  numerical 
precision,  what  number  of  stars  should  be  regarded 
as  of  one  magnitude  and  what  of  another. 

An  idea  of  the  magnitude  of  a  star  can  be  readily 
gained  by  the  casual  observer.  Looking  at  the 
heavens  on  almost  any  cloudless  evening,  we  may 
assume  that  the  two,  three,  or  more  brightest  stars 
which  we  see  are  of  the  first  magnitude.  As  ex- 
amples of  those  of  the  second  magnitude,  may  be 
taken  the  five  brightest  stars  of  the  Dipper,  the  Pole 
Star,  and  the  brighter  stars  of  Cassiopeia.  Some  or 
all  of  these  objects  can  be  seen  on  any  clear  night  of 
the  year  in  our  latitude.  Stars  of  the  third  magni- 
tude are  so  numerous  that  it  is  difficult  to  select  any 
one  for  comparison.  The  brightest  star  of  the  Plei- 
ades is  really  of  this  magnitude,  but  it  does  not 
appear  so  in  consequence  of  the  five  other  stars  by 
which  it  is  surrounded.  At  a  distance  of  15°  from 
the  Pole  Star,  Beta  Ursa  Minoris  is  always  visible,  and 
may  be  distinguished  by  being  slightly  redder  than 


1 8  MAGNITUDES  OF  THE  STARS 

the  Pole  Star;  it  lies  between  two  fainter  stars,  the 
brighter  of  which  is  of  the  third  and  the  other  of  the 
fourth  magnitude.  The  five  readily  visible  but  fainter 
stars  of  the  Pleiades  are  about  of  the  fourth  magni- 
tude. Of  the  fifth  magnitude  are  the  faintest  stars 
which  are  easily  visible  to  the  naked  eye,  while  the 
sixth  comprises  those  which  are  barely  visible  with 
good  eyes. 

Modern  astronomers,  while  adhering  to  the  general 

system  which  has  come  down  to  them  from  ancient 

times,  have  sought  to  give  it  greater  defin- 

Conception  iteness.       Careful    study    showed    that    the 

of  actual  amount  of  light  corresponding  to  the 

Magnitude.   ,.„-  .       ,&  .     ,  v         .    &. 

different  magnitudes  varied  nearly  m  geo- 
metrical progression  from  one  magnitude  to  another, 
a  conclusion  which  accords  with  the  well-known  psy- 
chological law  that  the  intensity  of  sensation  varies 
by  equal  amounts  when  the  exciting  cause  varies 
in  geometrical  progression.  It  was  found  that  an 
average  star  of  the  fifth  magnitude  gave  between  two 
and  three  times  as  much  light  as  an  average  one 
of  the  sixth  ;  one  of  the  fourth  gave  between  two  and 
three  times  as  much  light  as  one  of  the  fifth  ;  and  so- 
on to  the  second.  In  the  case  of  the  first  magnitude, 
the  diversity  is  so  great  that  it  is  scarcely  possible  to 
fix  an  average  ratio.  Sirius,  for  example,  is  really 
six  times  as  bright  as  Altair,  which  is  commonly 
taken  as  a  standard  for  a  first-magnitude  star.  To 
give  precision  to  their  estimates,  modern  astronomers 
are  gradually  seeking  to  lay  the  subject  of  magnitudes 
on  an  exact  basis  by  defining  a  change  of  one  unit  in 


MODERN  CONCEPTION  OF  MAGNITUDE       19 

the   magnitude   as   corresponding  to  an   increase  of 
about  two  and  one-half  times  in  the  amount  of  lio-ht. 

fe 

If  the  practice  of  separating  the  visible  stars  into 
only  six  orders  of  magnitude  were  continued  without 
change,  we  should  still  have  the  anomaly  of  including 
in  one  class  stars  of  markedly  different  degrees  of 
brightness.  Some  more  than  twice  as  bright  as 
others  would  be  designated  as  of  the  same  magni- 
tude. Hence,  to  give  quantitative  exactness  to  the 
results,  a  magnitude  is  regarded  as  a  quantity  which 
may  have  any  value  whatever,  and  may  be  expressed 
by  decimals — tenths  or  even  hundredths.  Thus,  we 
may  have  stars  of  magnitude  5.0,  5.1,  5.2,  etc.,  or  we 
may  even  subdivide  yet  further  and  speak  of  stars 
having  magnitudes  5.11,  5.12,  etc.  Unfortunately, 
however,  there  is  as  yet  no  way  known  of  determin- 
ing the  amount  of  light  received  from  a  star  except 
by  an  estimate  of  its  effect  upon  the  eye.  Two  stars 
are  regarded  as  equal  when  they  appear  to  the  eye  of 
equal  brilliancy.  In  such  a  case  the  judgment  is  very 
uncertain.  Hence,  observers  have  endeavoured  to 
give  greater  precision  to  it  by  the  use  of  photo- 
meters,— instruments  for  measuring  quantities  of 
light.  But  even  with  this  instrument  the  observer 
must  depend  upon  an  estimated  equality  of  light  as 
judged  by  the  eye.  The  light  from  one  star  is  in- 
creased or  diminished  in  a  known  proportion  until  it 
appears  equal  to  that  of  another  star,  which  may  be 
an  artificial  one  produced  by  the  flame  of  a  candle. 
The  proportion  of  increase  or  diminution  shows  the 
difference  of  magnitude  between  the  two  stars. 


20  MAGNITUDES  OF  THE  STARS 

As  we  proceed  to  place  the  subject  of  photometric 
measures  of  star-light  on  this  precise  basis  we  find 
the  problem  to  be  a  complex  one.  In  the  first  place, 
not  all  the  rays  which  come  from  a  star  are  visible  to 
our  eyes  as  light.  But  all  the  radiance,  visible  or 
invisible,  may  be  absorbed  by  a  dark  surface,  and  will 
then  show  its  effect  by  heating  that  surface.  The 
most  perfect  measure  of  the  radiance  of  a  star  would 
therefore  be  the  amount  of  heat  which  it  conveys, 
because  this  expresses  what  is  going  on  in  the  body 
better  than  the  amount  of  visible  light  can  do.  But 
unfortunately  the  heating  effect  of  the  rays  from  a 
star  is  below  what  can  be  measured  by  an  instrument. 
We  are  therefore  obliged  to  abandon  any  thought  of 
determining  the  total  amount  of  radiation  and  con- 
fine ourselves  to  that  portion  which  we  call  light. 

Here,  when  we  aim  at  precision,  we  find  that  light, 
as  we  understand  it,  is  properly  measured  only  by  its 
effect  on  the  optic  nerve,  and  there  is  no  way  of 
measuring  this  effect  except  by  estimation.  Thus,  all 
the  photometer  can  do  is  to  give  us  the  means  of  in- 
creasing or  diminishing  the  light  from  one  star,  so 
that  we  can  make  it  equal  by  estimation  to  that  from 
some  other  star  or  source  of  light. 

The  difficulty  of  reaching  strict  results  in  this  way 
is  increased  by  the  fact  that  the  stars  differ  in  color. 
Effect  of  Two  lights  can  be  estimated  as  equal  with 
Colour  on  greater  precision  when  they  are  of  the  same 
Magnitude.  coiour  t^an  when  the}r  coiours  are  different. 

An  additional  source  of  uncertainty  is  brought  in  by 
what  is  known   as  the   Purkinje   phenomenon,  after 


PHO  TOGRAPHIC  MA  GNITUDES  2 1 

the  physicist  who  first  observed  it.  He  found  that  if 
we  took  two  lights  of  equal  apparent  brightness,  the 
one  red  and  the  other  green,  and  then  increased  or 
diminished  them  in  the  same  proportion,  they  would 
no  longer  appear  equal.  In  other  words,  the  geomet- 
rical axiom  that  halves  or  quarters  of  equal  quantities 
are  themselves  equal,  does  not  apply  to  the  effect 
of  light  on  the  eye*  When  the  lights  are  diminished 
the  green  will  look  brighter  than  the  red.  If  we  increase 
them  in  the  same  proportion,  the  red  will  look  brighter 
than  the  green.  In  other  words,  the  red  light  will,  to 
our  vision,  increase  or  fade  away  more  rapidly  with  a 
given  amount  of  change  than  the  green  light  will. 

It  is  found  in  recent  times  that  this  law  of  change 
does  not  extend  progressively  through  all  spectral 
colours.  It  is  true  that  as  we  pass  from  the  red  to  the 
violet  end  of  the  spectrum  the  yellow  fades  away  less 
rapidly  with  a  given  diminution  than  does  the  red,  and 
the  green  still  less  rapidly  than  the  yellow.  But  when 
we  pass  from  the  green  to  the  blue,  it  is  said  that  the 
latter  does  not  fade  out  quite  so  fast  as  the  green. 

One  obvious  conclusion  from  all  this  is  that  two  stars 
of  different  colours  which  look  equal  to  the  naked  eye 
will  not  look  equal  in  the  telescope.  The  red  or  yellow 
star  will  look  relatively  brighter  in  a  telescope ;  the 
green  or  bluish  one  relatively  brighter  to  the  naked  eye. 

In  recent  times  stars  have  been  photographed  on  a 
large  scale.     Their  magnitudes  can  then  be          photo- 
determined  by  the  effect  of  the  light  on  the         graphic 
photographic  plate,  the  impression  of  the  Ma£mt 
star,  as  seen  in  a  microscope,  being  larger  and  more 


22  MAGNITUDES  OF  THE  STARS 

intense  as  the  star  is  brighter.  But  the  magnitude  thus 
determined  is  not  proportional  to  the  apparent  bright- 
ness as  seen  by  the  eye,  because  the  photographic 
effect  of  blue  light  is  much  greater  than  that  of  red 
light  having  the  same  apparent  brightness.  In  fact, 
the  difference  is  so  great  that,  with  the  chemicals  for- 
merly used,  red  light  was  almost  without  photographic 
effect.  Even  now,  what  we  measure  in  taking  the 
photograph  of  a  star  is  almost  entirely  the  light  in  the 
more  refrangible  portions  of  the  spectrum.  It  appears 
therefore  that  when  a  blue  and  a  yellow  star,  equally 
bright  to  the  naked  eye,  are  photographed,  the  impres- 
sion made  on  the  negative  by  the  blue  star  will  be 
greater  than  that  made  by  the  yellow  one.  A  distinc- 
tion is  therefore  recognised  between  photographic  and 
visual  magnitudes.  The  bluer  the  star,  the  brighter 
will  be  its  photographic  as  compared  with  its  visual 
magnitude. 

The  photographic  magnitudes  of  the  stars  are  now 
being  investigated  and  catalogued  on  a  scale  even 
larger  than  that  on  which  we  have  studied  the  visual 
magnitudes.  Yet  we  have  to  admit  the  non-corre- 
spondence of  the  two  systems.  The  most  that  can  be 
done  is  to  bring  about  the  best  attainable  agree- 
ment between  them  in  the  general  average  of  all  the 
stars. 

Fortunately  the  differences  between  the  colours  of 
the  stars  are  by  no  means  so  great  as  those  between 
the  colours  of  natural  objects  around  us.  All  the  stars 
radiate  light  of  all  colours  ;  and  although  the  colouring 
is  quite  appreciable  by  the  eye,  it  is  not  so  great  as  it 


SURVEYS  OF  THE  HEAVENS  23 

would  have  been  were  the  variations  in  colour  as  wide 
as  in  the  case  of  terrestrial  objects. 

Two  comprehensive  surveys  of  the  heavens,  in- 
tended to  determine  as  accurately  as  possible  the  mag- 
nitudes of  all  the  brighter  stars,  have  surveys  of 
recently  been  undertaken.  One  of  these  is  the  Heavens 
the  Harvard  photometry,  commenced  by  Professor 
Pickering  at  the  Harvard  Observatory,  and  now  ex- 
tended to  the  southern  hemisphere  by  the  aid  of  the 
branch  establishment  at  Arequipa,  Peru. 

The  instrument  designed  by  Professor  Pickering  for 
his  purpose  is  termed  a  meridian  photometer,  and  is 
so  arranged  that  the  observer  can  see  in  the  field  of 
his  telelcope  a  reflected  image  of  the  Pole  Star,  and, 
at  the  same  time,  the  image  of  some  other  star  while 
it  is  passing  the  meridian.  By  a  polarising  apparatus 
the  image  of  the  star  to  be  measured  is  made  to  appear 
of  equal  brightness  with  that  of  the  Pole  Star,  and  the 
position  of  a  Nicol  prism,  which  brings  out  this  equal- 
ity, shows  the  ratio  between  the  magnitudes  of  the  two 
stars. 

The  other  survey,  with  the  same  object,  is  now  being 
made  at  the  Potsdam  Astrophysical  Observatory,  near 
Berlin.  In  the  photometer  used  by  the  German  as- 
tronomers the  image  of  one  star  is  compared  with  an 
artificial  star  formed  by  the  flame  of  a  candle.  The 
work  is  performed  in  a  more  elaborate  way  than  at  the 
Harvard  Observatory,  and  in  consequence  only  that 
part  of  the  heavens  extending  from  the  equator  to  40° 
north  declination  has  been  completed  and  published. 
A  comparison  of  the  results  of  the  German  astrono- 


24  MAGNITUDES  OF  THE  STARS 

mers  with  those  of  Professor  Pickering  shows  a  curious 
difference  depending  on  the  colour  of  the  star.  In  the 
case  of  the  reddest  stars,  the  estimates  are  found  to 
be  in  fairly  close  agreement,  Pickering's  being  a  little 
the  fainter.  But  in  the  case  of  the  white  or  bluish 
stars,  the  estimates  of  the  German  astronomers  are 
more  than  one-fourth  of  a  magnitude  greater  than 
those  of  Pickering.  This  corresponds  to  a  change 
of  nearly  one-fourth  in  the  brightness.  Whether  this 
difference  is  to  be  regarded  as  purely  psychological, 
or  as  due  to  the  instruments  used,  is  an  interesting 
question  which  has  not  yet  been  settled.  It  is  diffi- 
cult to  conceive  how  different  instruments  should  give 
results  so  different.  On  the  one  hand,  the  compar- 
isons made  by  the  Germans  make  it  difficult  to  accept 
the  view  that  the  difference  is  due  purely  to  the  per- 
sonality of  the  observers.  There  are  two  German 
observers,  Drs.  Miillerand  Kempf,  whose  results  agree 
with  each  other  exactly.  On  the  other  hand,  Pritch- 
ard,  at  Oxford,  made  quite  an  extensive  photometric 
survey,  using  an  instrument  by  which  the  light  of  one 
star  was  cut  down  by  a  wedge-shaped  dark  glass, 
whereby  any  gradation  of  light  could  be  produced. 
A  comparison  shows  that  the  results  of  Pritchard  agree 
substantially  with  those  of  Pickering.  It  is  quite  pos- 
sible that  the  Purkinje  phenomenon  may  be  the  cause 
of  the  difference,  the  source  of  which  is  eminently 
worthy  of  investigation. 

It  must  not  be  supposed  from  this  that  such  estim- 
ates are  of  no  value  for  scientific  purposes.  Very 
important  conclusions,  based  on  great  numbers  of 


THE  LIGHT-RATIO  25 

stars,  may  be  drawn  even  from  these  uncertain  quan- 
tities. Yet,  it  can  hardly  be  doubted  that  if  the  light 
of  a  star  could  be  measured  from  time  to  time  to  its 
thousandth  part,  conclusions  of  yet  greater  value  and 
interest  might  be  drawn  from  the  measures. 

We  have  said  that  in  our  modern  system  the  aim 
has  been  to  so  designate  the  magnitudes  of  the  stars 
that  a  series  of  magnitudes  in  arithmetical  progression 
shall  correspond  to  quantities  of  light  ranging  in 
geometrical  progression.  We  have  also  said  that  a 
change  of  one  unit  of  magnitude  corresponds  to  a 
multiplication  or  division  of  the  light  by  about  2.5. 
On  any  scale  of  magnitude  this  factor  of  multiplica- 
tion is  called  the  light-ratio  of  the  scale.  In  recent 
times,  after  much  discussion  of  the  subject  and  many 
comparisons  of  photometric  measures  with  estimates 
made  in  the  old-fashioned  way,  there  is  a  general 
agreement  among  observers  to  fix  the  light-ratio  at 
the  number  whose  logarithm  is  0.4.  This  is  such  that 
an  increase  of  five  units  in  the  number  expressing  the 
magnitude  corresponds  to  a  division  of  the  light  by 
one  hundred.  If,  for  example,  we  take  a  standard  star 
of  magnitude  i  and  another  of  magnitude  6,  the  first 
would  be  one  hundred  times  as  bright  as  the  second. 
This  corresponds  to  a  light-ratio  slightly  greater 
than  2.5. 

When  this  scale  is  adopted,  the  series  of  magnitudes 
may  extend  indefinitely  in  both  directions  so  that  to 
every  apparent  brightness  there  will  be  a  certain  mag- 
nitude. For  example,  if  we  assign  the  magnitude 
i.o  to  a  certain  star,  taken  as  a  standard,  which 


26  MAGNITUDES  OF  THE  STARS 

would  formerly  have  been  called  a  star  of  the  first 
magnitude,  then  a  star  a  little  more  than  2.5  times  as 
bright  would  be  of  a  magnitude  one  less  in  number, 
that  is,  of  magnitude  o.  The  one  next  brighter  in  the 
series  would  be  of  magnitude-  i.  So  great  is  the  di- 
versity in  the  brightness  of  the  stars  formerly  called  of 
the  first  magnitude  that  Sirius  is  yet  brighter  than 
the  star  just  supposed,  the  number  expressing  its 
magnitude  being-  1.4. 

This  suggests  what  we  may  regard  as  one  of  the 
capital  questions  in  celestial  photometry.  There 
being  no  limit  to  the  extent  of  the  photometric  scale, 
stellar  what  would  be  the  stellar  magnitude  of  the 
Magnitude  sun  as  we  see  it  when  expressed  in  this  way 
of  the  Sun.  ofl  the  scale  ?  Such  a  numDer  is  readily  de- 
rivable when  we  know  the  ratio  between  the  light  of 
the  sun  and  that  of  a  star  of  known  magnitude.  Many 
attempts  have  been  made  by  observers  to  obtain  this 
ratio ;  but  the  problem  is  one  of  great  difficulty,  and 
the  results  have  been  extremely  discordant.  Amongst 
them  there  are  three  which  seem  less  liable  to  error 
than  others  :  those  of  Wollaston,  Bond,  and  Zollner. 
Their  results  for  the  stellar  magnitude  of  the  sun  are 
as  follows  : 

Wollaston —  26.6 

Bond —  25.8 

Zollner -26.6 

Of  these,  Zollner's  seems  to  be  the  best,  and  may, 
therefore,  in  taking  the  mean,  be  entitled  to  double 
weight.  The  result  will  then  be  : 

Stellar  magnitude  of  sun — 26.4 


STELLAR  MAGNITUDE  OF  THE  SUN  27 

From  this  number  may  be  readily  computed  the 
ratio  of  sunlight  to  that  of  a  star  of  any  given  magni- 
tude. We  thus  find  : 

The  sun  gives  us  : 

10,000,000,000  times  the  light  of  Sirius. 
91,000,000,000  times  the  light  of  a  star  of  magnitude  i. 
9,100,000,000,000  times  the  light  of  a  star  of  magnitude  6. 

The  square  roots  of  these  numbers  show  the  num- 
ber of  times  we  should  increase  the  actual  distance  of 
the  sun  in  order  that  it  might  shine  as  a  star  of  the 
corresponding  magnitude.  These  numbers  and  the 
corresponding  parallax  are  as  follows  : 


Sirius;  Distance=     100,000 

Parallax  =  2".o6 

Mag.  i                         302,000 

o".-68 

2         "               479,000 

o"-43 

3                         759i°°° 

0*27 

"        4            "                 1,202,000 

°".i7 

"     5        "           1,906,000 

o".n 

"      6         "            3,020,000 

o".o7 

These  parallaxes  are  those  that  the  sun  would  have 
if  placed  at  such  a  distance  as  to  shine  with  the 
brightness  indicated  in  the  first  column.  They  are 
generally  larger  than  those  of  stars  of  the  corre- 
sponding magnitudes,  from  which  we  conclude  that  the 
sun  is  smaller  than  the  brighter  of  the  stars. 


CHAPTER  III 

CONSTELLA  TION  AND  STAR  NAMES 

Now  came  still  evening  on,  and  twilight  grey 
Had  in  her  sober  livery  all  things  clad. 
.     .     .     now  glowed  the  firmament 
With  living  sapphires  ;  Hesperus  that  led 
The  starry  host  rode  brightest. — MILTON. 

IT  is  strongly  recommended  to  the  reader  to  study 
the  constellations  for  himself.  If  he  desires  to  feel 
all  the  sublimity  associated  with  them,  he  must  not 
be  satisfied  with  the  hurried  glance  or  occasional  sur- 
vey to  which  one  commonly  confines  himself  in  his 
evening  walk.  What  he  should  do  is,  on  a  clear  and 
moonless  summer  evening,  to  escape  from  his  usual 
surroundings,  and  go  to  a  place,  whether  field  or 
housetop,  where  there  is  nothing  to  obstruct  his 
vision,  or  disturb  the  current  of  his  thoughts.  There 
he  must  recline  on  his  back,  so  as  to  take  in  as  much 
as  possible  of  the  starry  vault  at  one  view.  One 
doing  this  for  the  first  time  will  be  surprised  at  the 
magnificence  of  the  spectacle.  As  he  looks  upon  the 
"  universal  frame  "  and  reflects  that  it  has  stood  as  he 
now  sees  it  through  ages  compared  with  which  the 
whole  period  of  human  history  is  but  a  fleeting 
28 


STUDY  OF  THE  CONSTELLATIONS  29 

moment,  the  mind  will  be  filled  with  a  consciousness 
of  infinity  and  eternity  which  never  before  entered  it. 
Other  sights  become  stale  from  custom,  but  this  can 
never  lose  its  relish.  It  can  be  enjoyed  without 
knowing  the  name  of  a  constellation,  but  is  more 
impressive  when  one  reflects  that  the  eyes  of  man 
have  gazed  upon,  and  studied  it  ever  since  our  race 
appeared  on  earth. 

In  ancient  times  the  practice  was  adopted  of  im- 
agining the  figures  of  heroes  and  animals  to  be  so 
outlined  in  the  heavens  as  to  include  in  each  figure  a 
large  group  of  the  brighter  stars.  In  a  few  cases 
some  vague  resemblance  may  be  traced  between  the 
configurations  of  the  stars  and  the  features  of  the 
object  they  are  supposed  to  represent ;  in  general, 
however,  the  object  chosen  seems  quite  arbitrary. 
One  animal  or  man  could  be  fitted  in  as  well  as 
another.  There  is  no  historic  record  as  to  the  time 
when  the  constellations  were  mapped  out,  or  of  the 
process  by  which  the  outlines  were  traced.  The 
names  of  heroes,  such  as  Perseus,  Cepheus,  Hercules, 
etc.,  intermingled  with  the  names  of  goddesses,  show 
that  the  time  was  probably  during  the  heroic  age. 
No  maps  are  extant  showing  exactly  how  each  figure 
was  placed  in  the  constellation  ;  but  in  the  catalogue 
of  stars  given  by  Ptolemy  in  his  Almagest,  the  posi- 
tions of  particular  stars  on  the  supposed  body  of  the 
hero,  goddess,  or  animal  are  designated.  For  exam- 
ple, Aldebaran  is  said  to  have  formed  the  eye  of  the 
Bull.  Two  stars  marked  the  right  and  left  shoulders 
of  Orion,  and  a  small  cluster  marked  the  position  of 


30         CONSTELLATIONS  AND  STAR  NAMES 

his  head.  A  row  of  three  stars  in  a  horizontal  line 
showed  his  belt,  three  stars  in  a  vertical  line  below 
them  his  sword.  From  these  statements  the  position 
of  the  figure  can  be  reproduced  with  a  fair  degree  of 
certainty. 

In  the  well-known  constellation  Ursa  Major,  the 
Great  Bear,  familiarly  known  as  "  the  Dipper,"  three 
stars  form  the  tail  of  the  animal,  and  four  others 
a  part  of  his  body.  This  formation  is  not  unnatural, 
yet  the  figure  of  a  dipper  fits  the  stars  much  better 
than  that  of  a  bear.  In  Cassiopeia,  which  is  on  the 
opposite  side  of  the  pole  from  the  Dipper,  the  brighter 
stars  may  easily  be  imagined  to  form  a  chair  in  which 
a  lady  may  be  seated.  As  a  general  rule,  however, 
the  resemblances  of  the  stars  to  the  figure  are  so 
vague  that  the  latter  might  be  interchanged  to  any 
extent  without  detracting  from  their  appropriate- 
ness. 

In  any  case,  it  was  impossible  so  to  arrange  the 
figures  that  they  should  cover  the  entire  heavens  ; 
blank  spaces  were  inevitably  left  in  which  stars  might 
be  found.  In  order  to  include  every  star  in  some 
constellation,  the  figures  have  been  nearly  ignored  by 
modern  astronomers,  and  the  heavens  have  been 
divided  up,  by  somewhat  irregular  lines,  into  patches, 
each  of  which  contains  the  entire  figure  as  recognised 
by  ancient  astronomers.  But  all  are  not  agreed  as 
to  the  exact  outlines  of  these  extended  constellations, 
and,  accordingly,  a  star  is  sometimes  placed  in  one 
constellation  by  one  astronomer  and  in  another  con- 
stellation by  another. 


THE  SOUTHERN  CONSTELLATIONS  31 

The  confusion  thus  arising  is  especially  great  in 
the  southern  hemisphere,  where  it  has  been  intensified 
by  the  subdivision  of  one  of  the  old  con- 
stellations.     The  ancient  constellation  Argo     southern 
covered  so  large  a  region  of  the  heavens,   Consteiia- 

1-111  •  tions. 

and    included    so    many   conspicuous    stars, 

that  it  was  divided  into   four,   representing  various 

parts  of  a  ship — the  sail,  the  poop,  the  prow,  and  the 

hull. 

Dr.  Gould,  while  director  of  the  Cordoba  Observa- 
tory, during  the  years  1870  to  1880,  constructed  the 
Uranometria  Argentina,  in  which  all  the  stars  visible 
to  the  naked  eye  from  the  south  pole  to  a  parallel  of 
declination  ten  degrees  north  of  the  celestial  equator 
were  catalogued  and  mapped.  He  made  a  revision 
of  the  boundaries  of  each  constellation  in  such  a  way 
as  to  introduce  greater  regularity.  The  rule  gener- 
ally followed  was  that  the  boundaries  should,  so  far 
as  possible,  run  in  either  an  east-and-west  or  a  north- 
and-south  direction  on  the  celestial  sphere.  They 
were  so  drawn  that  the  smallest  possible  change 
should  be  made  in  the  notation  of  the  conspicuous 
stars ;  that  is,  the  rule  was  that,  if  possible,  each 
bright  star  should  be  in  the  same  constellation  as 
before.  The  question  whether  this  new  division  shall 
replace  the  ancient  one  is  one  on  which  no  consensus 
of  view  has  yet  been  reached  by  astronomers.  Sim- 
plicity is  undoubtedly  introduced  by  Gould's  arrange- 
ment ;  yet,  in  the  course  of  time,  owing  to  precession, 
the  lines  on  the  sphere  which  now  run  north  and 
south  or  east  and  west  will  no  longer  do  so,  but  will 


32          CONSTELLATIONS  AND  STAR  NAMES 

deviate  almost  to  any  extent.  The  only  advantage 
then  remaining  will  be  that  the  bounding  lines  will 
generally  be  arcs  of  great  circles. 

When  the  heavens  began  to  be  carefully  studied, 
two  or  three  centuries  ago,  new  constellations  were 
introduced  by  Hevelius  and  other  astronomers  to  fill 
the  vacant  spaces  left  by  the  ancient  ones  of  Ptolemy. 
To  some  of  these  rather  fantastic  names  were  given  ; 
the  Bull  of  Poniatoivski,  for  example.  Some  of  these 
new  additions  have  been  retained  to  the  present  time, 
but  in  other  cases  the  space  occupied  by  the  proposed 
new  constellation  was  filled  up  by  extending  the 
boundaries  of  the  older  ones. 

At  the  present  time  the  astronomical  world,  by 
common  consent,  recognises  eighty-nine  constellations 
in  the  entire  heavens.  In  this  enumeration  Argo  is 
not  counted,  but  its  four  subdivisions  are  taken  as 
separate  constellations. 

A  glance  at  the  heavens  will  make  it  evident  that 
the  problem  of  designating  a  star  in  such  a  way  as  to 
Naming  distinguish  it  from  all  its  neighbours  must 
the  stars.  be  a  difficult  one.  If  such  be  the  case  with 
the  comparatively  small  number  of  stars  visible  to  the 
naked  eye,  how  must  it  be  with  the  vast  number  that 
can  be  seen  only  with  the  telescope  ?  In  the  case  of 
the  great  mass  of  telescopic  stars  we  have  no  method 
of  designation  except  by  the  position  of  the  star  and 
its  magnitude  ;  but  with  the  brighter  stars,  and,  in- 
deed, with  all  that  have  been  catalogued,  other  mean? 
of  identification  are  available. 

It  is  but  natural  to  give  a  special  name  to  a  con- 


NAMING  THE  STARS  33 

spicuous  star.  That  this  was  done  in  very  early 
antiquity  we  know  by  the  allusion  to  Arcturus  in  the 
Book  of  Job.  At  least  two  such  names,  Castor  and 
Pollux,  have  come  down  to  us  from  classical  antiquity, 
but  most  of  the  special  names  given  to  the  stars  in 
modern  times  are  corruptions  of  certain  Arabic  desig- 
nations. As  an  example  we  may  mention  Aldebaran, 
a  corruption  of  A I  Dabaran  —  The  Follower.  There 
is,  however,  a  tendency  to  replace  these  special  names 
by  a  designation  of  the  stars  on  a  system  devised  by 
Bayer  early  in  the  seventeenth  century. 

This  system  of  naming  stars  is  quite  analogous  to 
our  system  of  designating  persons  by  a  family  name 
and  a  Christian  name.  The  family  name  of  a  star  is 
that  of  the  constellation  to  which  it  belongs.  The 
Christian  name  is  a  letter  of  the  Greek  or  Roman 
alphabet  or  a  number.  As  any  number  of  men  in 
different  families  may  have  the  same  Christian  name, 
so  the  same  letter  or  number  may  be  assigned  to  stars 
in  any  number  of  constellations  without  confusion. 

The  work  of  Bayer  was  published  under  the  title  of 
Uranometria,  of  which  the  first  edition  appeared  in 
1 60 1.  This  work  consists  mainly  of  maps  of  the  stars. 
In  marking  the  stars  with  letters  on  the  map,  the  rule 
followed  seems  to  have  been  to  give  the  brighter 
stars  the  earlier  letters  in  the  alphabet.  Were  this 
system  followed  absolutely,  the  brightest  star  should 
always  be  called  Alpha ;  the  next  in  order  Beta,  etc. 
But  this  is  not  always  the  case.  Thus  in  the  constella- 
tion Gemim,ihe  brightest  star  is  Pollux,  which  is  marked 
Beta,  while  Alpha  is  the  second  brightest.  What  sys* 


34  CONSTELLATION  AND  STAR  NAMES 

tern,  if  any,  Bayer  adopted  in  detail  has  been  a  subject 
of  discussion,  but  does  not  appear  to  have  been  satis- 
factorily made  out.  Quite  likely  Bayer  himself  did  not 
attempt  accurate  observations  on  the  brightness  of  the 
stars,  but  followed  the  indications  given  by  Ptolemy 
or  the  Arabian  astronomers.  As  the  number  of  stars 
to  be  named  in  several  constellations  exceeds  the 
number  of  letters  in  the  Greek  alphabet,  Bayer  had 
recourse,  after  the  Greek  alphabet  was  exhausted,  to 
letters  of  the  Roman  alphabet.  In  this  case  the  letter 
A  was  used  as  a  capital,  in  order,  doubtless,  that  it 
should  not  be  confounded  with  the  Greek  a.  In  other 
cases  small  italics  are  used.  In  several  catalogues 
since  Bayer,  new  italic  letters  have  been  added  by 
various  astronomers.  Sometimes  these  have  met  with 
general  acceptance,  and  sometimes  not. 

Flamsteed  was  the  first  Astronomer  Royal  of  Eng- 
land, and  observed  at  Greenwich  from  1666  to  1715. 
Among  his  principal  works  is  a  catalogue  of  stars  in 
which  the  positions  are  given  with  greater  accuracy 
than  had  been  attained  by  his  predecessors.  He 
slightly  altered  the  Bayer  system  by  introducing 
numbers  instead  of  Greek  letters.  This  had  the  ad- 
vantage that  there  was  no  limit  to  the  number  of  stars 
which  could  be  designated  in  each  constellation.  He 
assigned  numbers  to  all  the  brighter  stars  in  the  order 
of  their  right  ascension,  irrespective  of  the  letters 
used  by  Bayer.  These  numbers  are  extensively  used 
to  the  present  day,  and  will  doubtless  continue  to  be 
the  principal  designations  of  the  stars  to  which  they 
refer.  It  is  very  common  in  our  modern  catalogues 


NAMING   THE  STARS  35 

to  give  both  the  Bayer  letter  and  the  Flamsteed 
number  in  the  case  of  Bayer  stars. 

The  catalogues  by  Flamsteed  do  not  include  quite 
all  the  stars  visible  to  the  naked  eye  ;  but  various 
uranometries  have  been  published  which  were  intended 
to  include  all  such  stars.  In  such  cases  the  designations 
now  used  frequently  correspond  to  the  numbers  given 
in  the  uranometries  of  Bode,  Argelander,  and  Heis. 

In  recent  times  these  uranometries  have  been  sup- 
plemented by  censuses  of  the  stars,  which  are  intended 
to  include  all  the  stars  to  the  ninth  or  tenth  magni- 
tude. I  shall  speak  of  these  in  the  next  section  ;  at 
present  it  will  suffice  to  say  that  stars  are  very  gener- 
ally designated  by  their  place  in  such  a  census. 

There  is  still  here  and  there  some  confusion  both  as 
to  the  boundaries  of  the  constellations  and  as  to  the 
names  of  a  few  of  the  stars  in  them.  I  have  already 
remarked  that,  in  drawing  the  imaginary  boundaries 
on  a  star  map,  as  representing  the  celestial  sphere, 
different  astronomers  have  placed  the  lines  differently. 
One  of  the  regions  in  which  this  is  especially  true  is 
in  the  neighbourhood  of  the  north  pole,  where  some 
astronomers  place  stars  in  the  constellation  Cepheus 
which  others  place  in  Ursa  Minor.  Hence  in  the 
Bayer  system  the  same  star  may  have  different  names 
in  different  catalogues.  Again,  in  extending  the 
names  or  numbers,  some  astronomers  use  names 
which  others  do  not  regard  as  authoritative.  The  re- 
mapping of  the  southern  hemisphere  by  Dr.  Gould 
changed  the  boundaries  of  most  of  the  southern  con- 
stellations in  a  way  already  mentioned. 


36  CONSTELLA  TION  AND  STAR  NAMES 

I  have  spoken  of  the  subdivision  of  the  great  con- 
stellation Argo  into  four  separate  ones.  Bayer  having 
assigned  to  the  principal  stars  in  this  constellation  the 
Greek  letters  alpha,  beta,  gamma,  etc.,  the  general 
practice  among  astronomers  since  the  subdivision  has 
been  to  continue  the  designation  of  the  stars  thus 
marked  as  belonging  to  the  constellation  Argo.  Thus, 
for  example,  we  have  Alpha  Argus,  which  after  the 
subdivision  belonged  to  the  constellation  Carina.  The 
variable  star  Eta  Argus  also  belongs  to  the  constella- 
tion Carina.  But  in  the  case  of  stars  not  marked  by 
Bayer,  the  names  were  assigned  according  to  the  sub- 
divided constellations,  Vela,  Carina,  etc.  Confusing 
though  this  proceeding  may  appear  to  be,  it  is  not  pro- 
ductive of  serious  trouble.  The  main  point  is  that  the 
same  star  should  always  have  the  same  name  in  suc- 
cessive catalogues.  Still,  however,  it  has  recently 
become  quite  common  to  ignore  the  constellation 
Argo  altogether  and  use  only  the  names  of  its  sub- 
divisions. The  reader  must  therefore  be  on  his  guard 
against  any  mistake  arising  in  this  way  in  the  study 
of  astronomical  literature. 

In  star  catalogues  the  position  of  a  star  in  the  heav- 
ens is  sometimes  given  in  connection  with  its  name. 
In  this  case  the  confusion  arising  from  the  same  star 
having  different  names  may  be  avoided,  since  a  star 
can  always  be  identified  by  its  right  ascension  and 
declination.  The  fact  is  that,  so  far  as  mere  identifi- 
cation is  concerned,  nothing  but  the  statement  of  a 
star's  position  is  really  necessary.  Unfortunately,  the 
position  constantly  changes  through  the  precession  of 


NAMING    THE  STARS  37 

the  equinoxes,  so  that  this  designation  of  a  star  is  a 
variable  quantity.  Hence  the  special  names  which  we 
have  described  are  the  most  convenient  to  use  in  the 
case  of  well-known  stars.  In  other  cases  a  star  is 
designated  by  its  number  in  some  well-known  cata- 
logue. But  even  here  different  astronomers  choose 
different  catalogues,  so  that  there  are  still  different 
designations  for  the  same  star.  The  case  is  one  in 
which  uniformity  of  practice  is  unattainable. 


2C4S23 


CHAPTER  IV 

CATALOGUING    AND    NUMBERING    THE  STARS 

Canst  thou  bind  the  sweet  influences  of  Pleiades,  or  loose  the  bands  of 
Orion  ?  Canst  thou  bring  forth  Mazzaroth  in  his  season  ?  Or  canst  thou  guide 
Arcturus  with  his  sons? — JOB. 

A  CATALOGUE  or  list  of  stars  is  a  work  giving  for 
**  each  star  listed  its  magnitude  and  its  position  on 
the  celestial  sphere,  with  such  other  particulars  as  may 
be  necessary  to  attain  the  object  of  the  catalogue.  If 
the  latter  includes  only  the  more  conspicuous  stars,  it 
is  common  to  add  the  name  of  each  star  that  has  one  ; 
if  none  is  recognised,  the  constellation  to  which  the 
star  belongs  is  frequently  given. 

The  position  of  a  star  on  the  celestial  sphere  is  de- 
fined by  its  right  ascension  and  declination.  These 
Right  As-  correspond  to  the  longitude  and  latitude  of 
cension  and  places  on  the  earth  in  the  following  way  : 
Declination.  jmag|ne  a  piane  passing  through  the  centre 
of  the  earth  and  coinciding  with  its  equator,  to 
extend  out  so  as  to  intersect  the  celestial  sphere.  The 
line  of  intersection  will  be  a  great  circle  of  the  celes- 
tial sphere,  called  the  celestial  equator.  The  axis  of 
the  earth,  being  also  indefinitely  extended  in  both  the 
38 


RIGHT  ASCENSION  AND  DECLINA  TION       39 

north  and  the  south  directions,  will  meet  the  celestial 
sphere  in  two  opposite  points,  known  as  the  north 
and  south  celestial  poles.  The  equator  will  then  be 
a  great  circle  90°  from  each  pole.  Then  as  meridians 
are  drawn  from  pole  to  pole  on  the  earth,  cutting  the 
equator  at  different  points,  so  imaginary  meridians  are 
conceived  as  drawn  from  pole  to  pole  on  the  celestial 
sphere.  Corresponding  to  parallels  of  latitude  on 
the  earth  we  have  parallels  of  declination  on  the  celes- 
tial sphere.  These  are  parallel  to  the  equator,  and 
become  smaller  and  smaller  as  we  approach  either  pole. 
The  correspondence  of  the  terrestrial  and  celestial  cir- 
cles is  this  : 

To  latitude  on  the  earth's  surface  corresponds  declin- 
ation in  the  heavens. 

To  longitude  on  the  earth  corresponds  right  ascen- 
sion in  the  heavens. 

A  little  study  of  this  system  will  show  that  the  zenith 
of  any  point  on  the  earth's  surface  is  always  in  a  de- 
clination equal  to  the  latitude  of  the  place.  For  ex- 
ample, for  an  observer  in  Philadelphia,  in  40°  latitude, 
the  parallel  of  40°  north  declination  will  always  pass 
through  his  zenith,  and  a  star  of  that  declination  will, 
in  the  course  of  its  diurnal  motion,  also  pass  through 
his  zenith. 

So  also  to  an  observer  on  the  equator  the  celestial 
equator  always  passes  through  the  zenith  and  through 
the  east  and  west  points  of  the  horizon. 

In  the  case  of  the  right  ascension,  the  relation  be- 
tween the  terrestrial  and  celestial  spheres  is  not  con- 
stant, because  of  the  diurnal  motion,  which  keeps  the 


40  CATALOGUING  AND  NUMBERING 

terrestrial  meridians  in  constant  revolution  relative  to 
the  celestial  meridians.  Allowing  for  this  motion, 
however,  the  system  is  the  same.  As  we  have  on  the 
earth's  surface  a  prime  meridian  passing  from  pole  to 
pole  through  the  Greenwich  Observatory,  so  in  the 
heavens  a  prime  meridian  passes  from  one  celestial 
pole  to  the  other  through  the  vernal  equinox.  Then 
to  define  the  right  ascension  of  any  star  we  imagine  a 
great  circle  passing  from  pole  to  pole  through  the  star, 
as  we  imagine  one  to  pass  from  pole  to  pole  through 
a  city  on  the  earth  of  which  we  wish  to  designate  the 
longitude.  The  actual  angle  which  this  meridian 
makes  with  the  prime  meridian  is  the  right  ascension 
of  the  star,  as  the  corresponding  angle  is  the  longi- 
tude of  the  city  on  the  earth's  surface. 

There  is,  however,  a  difference  in  the  unit  of  angu- 
lar measurement  commonly  used  for  right  ascensions 
in  the  heavens  and  longitude  on  the  earth.  In  as- 
tronomical practice,  right  ascension  is  very  generally 
expressed  by  hours,  twenty-four  of  which  make  a  com- 
plete circle,  corresponding  to  the  apparent  revolution 
of  the  celestial  sphere  in  twenty-four  hours.  The  rea- 
son of  this  is  that  astronomers  determine  right  ascen- 
sion by  the  time  shown  by  a  clock  so  regulated 
as  to  read  oh.  om.  os.  when  the  vernal  equinox 
crosses  the  meridian.  The  hour-hand  of  this  clock 
makes  a  revolution  through  twenty-four  hours  during 
the  time  that  the  earth  makes  one  revolution  on  its 
axis,  and  thus  returns  to  oh.  o m.  o s.  when  the 
vernal  equinox  again  crosses  the  meridian.  A  clock 
thus  regulated  is  said  to  show  sidereal  time.  Then 


ANCIENT  AND  MEDIEVAL  CATALOGUES     41 

the  right  ascension  of  any  star  is  equal  to  the  sidereal 
time  at  which  it  crosses  the  meridian  of  any  point  on 
the  earth's  surface.  Right  ascension  thus  designated 
in  time  may  be  changed  to  degrees  and  minutes  by 
multiplying  by  15.  Thus,  one  hour  is  equal  to  15° ; 
one  minute  of  time  is  equal  to  15'  of  arc,  and  one 
second  of  time  to  15"  of  arc. 

It  may  be  remarked  that  in  astronomical  practice 
terrestrial  longitudes  are  also  expressed  in  time,  the 
longitude  of  a  place  being  designated  by  the  number  of 
hours  it  may  be  east  or  west  of  Greenwich.  Thus, 
Washington  is  said  to  be  5h.  8m.  155.  west  of  Green- 
wich. This,  however,  is  not  important  for  our  present 
purpose. 

The  first  astronomer  who  attempted  to  make  a 
catalogue  of  all  the  known  stars  is  supposed  to  be 
Hipparchus,  who  flourished  about  150  B.C.  , 

r  J  Ancient  and 

There  is  an  unverified  tradition  to  the  effect  Mediaeval 
that  he  undertook  this  work  in  conse-  Catalogues 

,    ,  r  .  of  Stars. 

quence  01  the  appearance  ot  a  new  star  in 

the  heavens,  and  a  desire  to  leave  on  record,  for  the 

use    of    posterity,    such   information   respecting    the 

heavens  in  his  time  that  any  changes  which    might 

take  place  in  them  could  be  detected.     This  catalogue 

has  not  come  down  to  us — at  least  not  in  its  original 

form. 

Ptolemy,  the  celebrated  author  of  the  Almagest, 
flourished  A.D.  150.  His  great  work  contains  the 
earliest  catalogue  of  stars  which  we  have.  There 
seems  to  be  a  certain  probability  that  this  catalogue 
may  either  be  that  of  Hipparchus  adopted  by  Ptolemy 


42  CATALOGUING  AND  NUMBERING 

unchanged,  or  may  be  largely  derived  from  Hip- 
parchus.  This,  however,  is  little  more  than  a  sur- 
mise, due  to  the  fact  that  Ptolemy  does  not  seem  to 
have  been  a  great  observer,  but  based  his  theories 
very  largely  on  the  observations  of  his  predecessors. 
The  actual  number  of  stars  which  it  contains  is  1030. 
The  positions  of  these  are  given  in  longitude  and 
latitude,  and  are  also  described  by  their  places  in  the 
figure  of  the  constellation  to  which  each  may  belong. 
Not  unfrequently  the  longitude  or  latitude  is  a  degree 
or  more  in  error,  showing  that  the  instruments  with 
which  the  position  was  determined  were  of  rather 
rough  construction. 

So  far  as  the  writer  is  aware,  no  attempt  to  make  a 
new  catalogue  of  the  stars  is  found  until  the  tenth 
century.  Then  arose  the  Persian  astronomer,  Abd- 
Al-Rahman  Al-Sufi,  commonly  known  as  Al-Sufi, 
who  was  born  A.D.  903  and  lived  until  986.  Nothing 
is  known  of  his  life  except  that  he  was  a  man  cele- 
brated for  his  learning,  especially  in  astronomy.  His 
only  work  on  the  latter  subject  which  has  come  down 
to  us  is  a  description  of  the  fixed  stars,  which  was 
translated  from  the  Arabic  by  Schjellerup  and  pub- 
lished in  1874  by  the  St.  Petersburg  Academy  of 
Science.  This  work  is  based  mainly  on  the  catalogue 
of  Ptolemy,  all  the  stars  of  which  he  claimed  to  have 
carefully  examined.  But  he  did  not  add  any  new 
stars  to  Ptolemy's  list,  nor,  it  would  seem,  did  he  at- 
tempt to  redetermine  their  positions.  He  simply 
used  the  longitudes  and  latitudes  of  Ptolemy,  the 
former  being  increased  by  12°  42'  on  account  of  the 


ANCIENT  AND  MEDIEVAL  CATALOGUES     43 

precession  during  the  interval  between  his  time  and 
that  to  which  Ptolemy's  catalogue  was  reduced.  The 
translator  says  of  his  work  that  it  gives  a  description 
of  the  starry  heavens  at  the  time  of  the  author  and  is 
worthy  of  the  highest  confidence.  The  main  body 
of  the  work  consists  of  a  detailed  description  of  each 
constellation,  mentioning  the  positions  and  appear- 
ances of  the  stars  which  it  contains.  Here  we  find  the 
Arabic  names  of  the  stars,  which  were  not,  however, 
used  as  proper  names,  but  seem  rather  to  have  been 
Arabic  words  representing  some  real  or  supposed  pe- 
culiarity of  the  separate  stars,  or  arbitarily  applied  to 
them. 

Four  centuries  later  arose  the  celebrated  Ulugh 
Beigh,  grandson  of  Tamerlane,  who  reigned  at  Sam- 
arcand  in  the  middle  of  the  fifteenth  century.  Baily 
says  of  him : 

"  Ulugh  Beigh  was  not  only  a  warlike  and  powerful  monarch, 
but  also  an  eminent  promoter  of  the  sciences  and  of  learned  men. 
During  his  father's  lifetime  he  had  attracted  to  his  capital  all  the 
most  celebrated  astronomers  from  different  parts  of  the  world  ;  he 
erected  there  an  immense  college  and  observatory,  in  which  above 
a  hundred  persons  were  constantly  occupied  in  the  pursuits  of 
science,  and  caused  instruments  to  be  constructed  of  a  better 
form  and  greater  dimensions  than  any  that  had  hitherto  been  used 
for  making  astronomical  observations." 

His  fate  was  one  which  so  enlightened  a  promoter 
of  learning  little  deserved  :  he  was  assassinated  by 
the  order  of  his  own  son,  who  desired  to  succeed  him 
on  his  throne,  and,  in  order  to  make  his  position  the 
more  secure,  also  put  his  only  brother  to  death.  A 


44  CATALOGUING  AND  NUMBERING 

catalogue  of  the  stars  bears  the  name  of  this  monarch  ; 
he  is  supposed  to  have  made  many  or  most  of  the 
observations  on  which  it  is  founded.  Posterity  will 
be  likely  to  suppose  that  a  sovereign  used  the  eyes 
of  others  more  than  his  own  in  making  the  observa- 
tions. However  this  may  be,  his  catalogue  seems  to 
have  been  the  first  in  which  the  positions  of  the  stars 
given  by  Ptolemy  were  carefully  revised.  He  found 
that  there  were  twenty-seven  of  Ptolemy's  stars  too 
far  south  to  be  visible  at  Samarcand,  and  that  eight 
others,  although  diligently  looked  after,  could  not  be 
discovered.  It  is  curious  that,  like  Al-Sufi,  he  does 
not  seem  to  have  added  any  new  stars  to  Ptolemy's 
list. 

Next  in  the  order  of  time  comes  the  work  of  Bayer, 
whose  method  of  naming  the  stars  has  already  been 
described.  The  main  feature  of  his  work  consists  in 
maps  of  all  the  constellations.  Previous  to  his  time, 
celestial  globes,  made  especially  for  the  use  of  the 
navigator,  took  the  place  of  maps  of  the  stars.  The 
first  edition  of  this  book  was  published  in  1601,  and 
is  distinguished  by  the  fact  that  a  list  of  stars  in  each 
constellation  is  printed  on  the  backs  of  the  maps. 
Bayer  did  not  confine  himself  to  the  northern  hemi- 
sphere, but  extended  his  list  over  the  whole  celestial 
sphere,  from  the  north  to  the  south  pole. 

The  catalogue  of  the  celebrated  Tycho  Brahe,  pre- 
pared toward  the  end  of  the  sixteenth  century,  though 
of  great  historic  value,  is  of  no  special  interest  to  the 
general  reader  at  the  present  time.  A  supplement  to 
it,  continuing  its  list  of  stars  to  the  south  pole,  was 


MODERN  CATALOGUES  OF  STARS  45 

published  by  Halley,  who  made  the  necessary  observa- 
tions during  a  journey  to  St.  Helena  in  1677. 

The  catalogue  of  Hevelius,  published  in  1690,  offers 
no  feature  of  special  interest,  except  the  addition  of 
several  new  constellations,  which  he  placed  between 
those  already  known.  Having  the  aid  of  the  tele- 
scope, he  was  able  to  include  in  his  catalogue  stars 
which  had  been  invisible  to  his  predecessors. 

Modern  catalogues  of  the  stars  may  be  divided  into 
two  classes  :  Those  which  include  only  stars  of  a 
special  class,  or  stars  of  which  the  observer  Modern 
sought  to  determine  the  position  or  magni-  Catalogues 
tude  with  all  attainable  precision  ;  and  cata-  of  stars> 
logues  intended  to  include  all  the  stars  in  any  given 
region  of  the  heavens,  down  to  some  fixed  order 
of  magnitude.  It  may  appear  remarkable  that  no  at- 
tempt of  the  latter  sort  was  seriously  made  until  more 
than  two  centuries  after  the  telescope  had  been  pointed 
at  the  heavens  by  Galileo.  A  reason  for  the  absence 
of  such  an  attempt  will  be  seen  in  the  vast  number  of 
stars  shown  by  the  telescope,  the  difficulty  of  stopping 
at  any  given,  point,  and  the  seeming  impossibility  of 
assigning  positions  to  hundreds  of  thousands  of  stars. 
The  latter  difficulty  was  overcome  by  the  improved 
methods  of  observation  devised  in  modern  times. 

Catalogues  intended  to  be  complete  down  to  some 
given  magnitude  are  of  two  classes  :  Those  which 
include  only  the  stars  visible  to  the  naked  eye,  or 
with  a  small  opera-glass,  and  those  which  take  in  all 
the  stars  to  the  Qth  or  loth  magnitude. 

Those  of  the  first  class  are  mostly  published  in  con- 


46  CATALOGUING  AND  NUMBERING 

nection  with  star  maps,  and  are  sometimes  called 
"  uranometries."  For  that  portion  of  the  sky  visible 
in  our  latitudes  the  best  work  of  this  kind  is  Heis's 
Atlas  Ccelestis,  which  extends  to  magnitude  6.3. 

About  the  middle  of  the  nineteenth  century  the  cel- 
ebrated Argelander  commenced  the  work  of  actually 
cataloguing  all  the  stars  of  the  northern  celestial  hemi- 
sphere to  magnitude  9^.  This  work  was  termed  a 
Durchmusterung  of  the  northern  heavens,  a  term 
which  has  been  introduced  into  astronomy  generally 
to  designate  a  catalogue  in  which  all  the  stars  down 
to  the  gth  or  loth  magnitude  are  supposed  to  be 
mustered,  as  if  a  census  of  them  were  taken.  The 
work  fills  three  quarto  volumes  and  contains  more 
than  324,000  stars,  between  the  north  pole  and  2°  of 
south  declination,  of  each  of  which  the  magnitude 
and  the  right  ascension  and  declination  are  given. 
This  work  was  extended  by  Schonfeld,  Argelancler's 
assistant  and  successor,  to  22°  of  south  declination. 

In  the  latitudes  in  which  the  great  observatories  of 
the  northern  hemisphere  are  situated,  that  part  of  the 
celestial  sphere  within  40°  or  50°  of  the  south  pole 
always  remains  below  the  horizon.  Above  this  in- 
visible region  a  belt  of  somewhat  indefinite  breadth, 
10°  or  more,  can  be  only  imperfectly  observed,  owing 
to  the  nearness  of  the  stars  to  the  horizon,  and  the 
brevity  of  the  period  between  their  rising  and  setting. 
Up  to  the  middle  of  the  nineteenth  century,  the  few 
observatories  situated  in  the  southern  hemisphere 
were  too  ill-endowed  to  permit  of  their  undertaking  a 
complete  census  of  their  part  of  the  sky. 


THOME'S  DURCHMUSTERUNG  47 

The  first  considerable  work  emanating  from  the 
Cordoba  Observatory,  under  Gould,  was  the  Urano- 
metria  Argentina,  already  mentioned,  which  com- 
prised a  catalogue  of  all  the  stars  down  to  the  7th 
magnitude  from  the  south  pole  to  10°  of  north  de- 
clination. Another  work,  which  was  not  issued  until 
after  Dr.  Gould's  death,  was  devoted  to  photographs 
of  southern  clusters  of  stars. 

The  work  of  Argelander  is  being  continued  at  the 
Cordoba  Observatory  as  a  Durchmusterung  of  the 
southern  heavens.  It  commences  at  22°  of  south  de- 
clination, where  Schonfeld's  work  ended,  and  is  to  be 
continued  to  the  south  pole.  This  work  is  still  in- 
complete, but  three  volumes  have  been  published  by 
Thome,  extending  to  51°  of  south  declination.  It  is 
expected  that  the  fourth  is  approaching  completion. 
This  catalogue  is,  in  one  point  at  least,  more  com- 
plete than  that  of  Argelander  and  Schonfeld,  as  it 
contains  all  the  stars  down  to  the  tenth  magnitude' 
The  three  volumes  give  the  positions  and  magnitudes 
of  no  less  than  489,827  stars,  nearly  175,000  more 
than  the  catalogue  of  Argelander  gives  for  the  entire 
northern  hemisphere.  If  the  remaining  part  of  the 
heavens,  from  42°  to  the  south  pole,  is  equally  rich, 
it  will  contain  about  350,000  stars,  and  the  entire 
work  will  comprise  more  than  800,000  stars. 

The  Royal  Observatory  of  the  Cape  of  Good  Hope, 
under  the  able  and  energetic  direction  of  Dr.  David 
Gill,  has  carried  out  a  work  of  the  same  kind,  which 
is  remarkable  for  being  based  on  photography.  The 
history  of  this  work  is  of  great  interest.  In  1882 


48  CATALOGUING  AND  NUMBERING 

Gill  secured  the  aid  of  a  photographer  at  the  Cape  of 
Good  Hope  to  take  pictures  of  the  brilliant  comet 
of  that  year,  with  a  large  camera.  On  developing 
the  pictures  the  remarkable  discovery  was  made  that 
not  only  all  the  stars  visible  to  the  naked  eye,  but 
telescopic  stars  down  to  the  ninth  or  tenth  magnitude 
were  also  found  on  the  negatives.  This  remarkable 
result  suggested  to  Gill  that  here  was  a  new  and 
simple  method  of  cataloguing  the  stars.  It  was  only 
necessary  to  photograph  the  heavens  and  then  meas- 
ure the  positions  of  the  stars  on  the  glass  negatives, 
which  could  be  done  with  much  greater  ease  and  cer- 
tainty than  measures  could  be  made  on  the  positions 
of  the  actual  stars,  which  were  in  constant  apparent 
motion. 

As  soon  as  the  necessary  arrangements  could  be 
made  and  the  necessary  instruments  devised  and  put 
The  Cape  mto  successful  operation,  Gill  proceeded  to 
Durchmus-  the  work  of  photographing  the  entire  south- 
terung.  ern  neavens  frOm  1 8°  of  south  declination  to 
the  celestial  pole.  The  results  of  this  work  are  found 
in  the  Cape  Photographic  Durchmusterung,  a  work  in 
three  quarto  volumes,  in  which  the  astronomers  of  all 
future  time  will  find  a  permanent  record  of  the  south- 
ern heavens  towards  the  end  of  the  nineteenth  century. 
The  actual  work  of  taking  the  photographs  extended 
from  1887  to  1891.  This,  however,  was  far  from  being 
the  most  difficult  part  of  the  enterprise.  The  more 
arduous  task  of  measuring  the  positions  of  a  half- 
million  of  stars  on  the  negatives,  and  determining  the 
magnitude  of  each,  was  undertaken  by  Professor  J. 


THE  CAPE  DURCHMUSTERUNG  49 

C.  Kapteyn,  of  the  University  of  Groningen,  Holland, 
and  brought  to  a  successful  completion  in  the  year 
1899.' 

What  the  work  gives  is,  in  the  first  place,  the  mag- 
nitude and  approximate  position  of  every  star  photo- 
graphed. The  determining  of  the  magnitude  of  a 
star  from  its  photograph  is  an  important  and  delicate 
question.  There  is  no  difficulty  in  determining,  from 
the  diameter  of  the  image  of  the  star  as  seen  in  the 
microscope,  what  its  photographic  magnitude  was  at 
the  time  of  the  exposure,  as  compared  with  other 
stars  on  the  same  plate.  But  can  we  rely  upon  simi- 
lar photographic  magnitudes  on  different  plates  corre- 
sponding to  similar  brightnesses  of  the  stars  ?  In  the 
opinion  of  Gill  and  Kapteyn  we  cannot.  The  trans- 
parency of  the  air  varies  from  night  to  night,  and  on 
a  very  clear  night  the  same  star  will  give  a  stronger 
image  than  it  will  when  the  air  is  thick.  Besides, 
slightly  different  instruments  were  used  in  the  course 
of  the  work.  For  these  reasons  a  scale  of  magnitude 
was  determined  on  each  plate  by  comparing  the  pho- 
tographic intensity  of  the  images  of  a  number  of  stars 
with  the  magnitudes  as  observed  with  the  eye  by  vari- 
ous observers.  Thus  on  each  plate  the  magnitude 
was  reduced  to  a  visual  scale. 

It  does  not  follow  from  this  that  the  magnitudes 

1  This  work  of  Kapteyn  offers  a  remarkable  example  of  the  spirit  which  ani- 
mates the  born  investigator  of  the  heavens.  Although  the  work  was  officially 
that  of  the  British  Government,  the  years  of  toil  devoted  to  it  were,  as  the 
writer  understands,  expended  without  other  compensation  than  the  consciousness 
of  making  a  noble  contribution  to  knowledge,  and  the  appreciation  of  his  fel- 
low astronomers  of  this  and  future  generations. 
4 


50  CATALOGUING  AND  NUMBERING 

are  visual,  and  not  photographic.  It  is  still  true  that 
a  blue  star  will  give  a  much  stronger  photographic 
image  than  a  red  star  of  equal  visual  brightness.  In 
a  general  way,  it  may  be  said  that  the  category  in- 
cludes all  the  stars  to  very  nearly  the  tenth  magnitude, 
and  on  most  of  the  plates  stars  of  10.5  were  included. 
In  fact,  now  and  then  is  found  a  star  of  the  eleventh 
magnitude. 

A  feature  of  the  work  which  adds  greatly  to  its 
value  is  a  careful  and  exhaustive  comparison  of  its 
results  with  previous  catalogues  of  the  stars.  When 
a  star  is  found  in  any  other  catalogue  the  latter 
is  indicated.  Most  interesting  is  a  complete  list 
of  catalogued  stars  which  ought  to  be  on  the 
photographic  negatives,  but  were  not  found  there. 
Every  such  case  was  exhaustively  investigated. 
Sometimes  the  star  was  variable,  sometimes  it  was 
so  red  in  colour  that  it  failed  to  impress  itself 
on  the  plate,  sometimes  there  were  errors  in  the 
catalogue. 

The  great  enterprise  of  making  a  photographic  map 
of  the  heavens,  now  being  carried  on  as  an  interna- 
tional enterprise,  having  its  headquarters  at  Paris,  is 
yet  wider  in  its  scope  than  the  works  we  have  just 
described.  One  point  of  difference  is  that  it  is  in- 
tended to  include  all  the  stars,  however  faint,  that 
admit  of  being  photographed  with  the  instruments  in 
use.  The  latter  are  constructed  on  a  uniform  plan, 
the  aperture  of  each  being  34  centimetres,  or  13.4 
inches,  and  the  focal  length  343  centimetres.  Two  sets 
of  plates  are  taken,  one  to  include  all  the  stars  that  the 


NUMBERING  THE  STARS  51 

instrument  will  photograph,  and  the  other  only  to 
take  in  those  to  the  eleventh  magnitude.  Of  the  lat- 
ter it  is  intended  to  prepare  a  catalogue.  Some  por- 
tions of  the  German  and  English  catalogues  have 
already  been  published,  and  their  results  will  be  made 
use  of  in  the  course  of  the  present  work. 

Closely  connected  with  the  work  of  cataloguing 
the  stars  is  that  of  enumerating  them.  In  view  of 
what  may  possibly  be  associated  with  any  Numbering 
one  star  —  planets  with  intellectual  beings  the  stars, 
inhabiting  them  —  the  question  how  many  stars  there 
are  in  the  heavens  is  one  of  perennial  interest.  But 
beyond  the  general  statement  we  have  already  made, 
this  question 'does  not  admit  of  even  an  approximate 
answer.  The  question  which  we  should  be  able  to 
answer  is  this :  How  many  stars  are  there  of  each 
distinguishable  magnitude?  How  many  of  the  first 
magnitude,  of  the  second,  of  the  third,  and  so  on  to 
the  smallest  that  have  been  estimated  ?  Even  in  this 
form  we  cannot  answer  the  question  in  a  way  which 
is  at  the  same  time  precise  and  satisfactory.  One 
magnitude  merges  into  another  by  insensible  grada- 
tions, so  that  no  two  observers  will  agree  as  to 
where  the  line  should  be  drawn  between  them.  The 
difficulty  is  enhanced  by  the  modern  system  —  very 
necessary,  it  is  true  —  of  regarding  magnitude  as  a 
continuously  varying  quantity  and  estimating  it  with 
all  possible  precision.  In  adjusting  the  new  system 
to  the  old  one,  it  may  be  assumed  that  an  average 
star  of  any  given  magnitude  on  the  old  system  would 
be  designated  by  the  corresponding  number  on  the 


5.2  CATALOGUING  AND  NUMBERING 

new  system.  For  example,  an  average  star  of  the 
fourth  magnitude  would  be  called  4.0 ;  one  of  the  fifth, 
5.0,  etc.  Then  the  brightest  stars  which  formerly 
were  called  of  the  fourth  magnitude,  would  now  be,  if 
the  estimate  were  carried  to  hundredths,  3.50,  while 
the  faintest  would  be  4.50.  What  were  formerly  called 
stars  of  the  fifth  magnitude  would  range  from  4.50  to 
5.50,  and  so  on.  But  we  meet  with  a  difficulty  when 
we  come  to  the  sixth  magnitude.  On  the  modern  sys- 
tem, magnitude  6.0  represents  the  faintest  star  visible 
to  the  naked  eye ;  but  the  stars  formerly  included 
in  this  class  would,  on  the  average,  be  somewhat 
brighter  than  this,  because  none  could  be  catalogued 
except  those  so  visible. 

The  most  complete  enumeration  of  the  lucid  stars 
by  magnitudes  has  been  made  by  Pickering  (Annals 
of  the  Harvard  Observatory,  vol.  xiv.).  The  stars 
were  classified  by  half-magnitudes,  calling 

M.        M. 

Mag.  2.0  all  from  1.75  to  2.25 
"      2.5    "  2.25  to  2.75,  etc. 


For  the  northern  stars,  Pickering  used  the  Harvard 
Photometry ;  for  the  southern,  Gould's  Uranometria 
Number  Argentina,  A  zone  from  the  equator  to  30° 
of  stars,  south  declination  is  common  to  both  ;  for  this 
zone  I  use  Gould.  The  number  of  each  class  in  the 
entire  sky,  north  and  south  of  the  celestial  equator,  is 
as  follows: 


NUMBER  OF  STARS 


53 


Mag. 
i± 

2.0 

2-5 

3-° 
3-5 
4.0 

4-5 
5-° 
5-5 
6.0 


Northern          Southern 
Hemisphere.     Hemisphere. 
Pickering.  Gould. 


9 

17 
17 

37 

61 

114 

228 
450 
787 
789 


i4 
15 
24 

74 
126 

234 

426 

68 1 

1189 


Total. 
23 
32 

78 

240 

462 

876 
1468 
1978 


Sum        2509  2824  5333 

It  would  seem  from  this  that  the  number  of  lucid 
stars  in  the  southern  celestial  hemisphere  is  315 
greater  than  in  the  northern.  But  this  arises  wholly 
from  a  seemingly  greater  number  of  stars  of  magni- 
tude 6.  In  the  zone  o°  to  30°  S.,  Pickering  has  214 
stars  of  this  class  fewer  than  Gould.  Hence  it  is  not 
likely  that  there  is  really  any  greater  richness  of  the 
southern  sky. 

The  total  number  of  lucid  stars  is  thus  found  to  be 
5333.  But  it  is  not  likely  that  stars  of  magnitudes 
6.1  and  6.2  should  be  included  in  this  class,  though 
this  is  done  in  the  above  table.  From  a  careful 
study  and  comparison  of  the  same  data  from  Picker- 
ing and  Gould,  Schiaparelli  numerated  the  stars  to 
magnitude  6.0.  He  found  : 

North  pole  to  30°  S  ____  .  ...................  3113  stars 

30°  S.  to  south  pole  ..............  o  .........  1190     ' 

Total  lucid  stars  .........................  43°3 


54  CATALOGUING  AND  NUMBERING 

For  most  purposes  a  classification  by  entire  magni- 
tudes is  more  instructive  than  one  by  half-magnitudes. 
From  the  third  magnitude  downward  we  may  assume 
that  forty  per  cent,  of  the  stars  of  each  half-magni- 
tude belong  to  the  magnitude  next  above,  and  sixty 
per  cent,  to  that  next  below.  We  thus  find  that  of 

Total. 
Mag.  o  and  i  there  are  21  stars 21 

;  2  5*  ;:  73  . 

3  157          230 

4  5°6     '!     736 

5  "  174°     "     2476 

1    6  "  5171      '     7647 

Here  it  is  to  be  remarked  that  under  magnitude  6 
are  included  many  other  than  the  lucid  stars,  namely, 
all  down  to  magnitude  6.4.  The  last  column  gives 
the  entire  number  of  stars  down  to  each  order  of 
magnitude. 

It  will  be  remarked  that  the  number  of  stars  of 
each  order  is  between  three  and  four  times  that  of 
the  order  next  brighter.  How  far  does  this  law  ex- 
tend? Argelander's  Durchmusterung,  which  is  sup- 
posed to  include  all  stars  to  magnitude  9.5,  gives 
315,039  stars  for  the  northern  hemisphere,  from 
which  it  would  be  inferred  that  the  whole  sky  con- 
tains 630,000  stars  to  the  ninth  magnitude.  Com- 
paring this  with  the  number,  764.7,  of  stars  to  the 
magnitude  6.5,  we  see  that  it  is  fortyfold,  so  that  it 
would  require  a  ratio  of  about  3.5  from  each  mag- 
nitude to  the  next  lower.  But  it  is  now  found  that 
Argelander's  list  contains,  in  the  greal&r  part  of  the 
heavens,  all  the  stars  to  the  tenth  magnitude. 


NUMBER  OF  STARS  55 

On  the  other  hand,  Thome's  Cordoba  Durchmus- 
terung  gives  340,380  stars  between  the  parallels  —  22° 
and  —42°.  This  is  0.14725  of  the  whole  sky,  so 
that,  on  Thome's  scale  of  magnitude,  there  are  about 
2,311,000  stars  to  the  tenth  magnitude  in  the  sky. 
This  is  more  than  three  times  the  Argelander  num- 
ber to  the  ninth  magnitude.  There  is,  therefore,  no 
evidence  of  any  falling  off  in  the  ratio  of  increase  up 
to  the  tenth  magnitude. 


CHAPTER  V 
THE  SPECTRA  OF  THE  STARS 

No  unregarded  star 

Contracts  its  light 
Into  so  small  a  character, 

Removed  far  from  our  humane  sight, 

But  if  we  steadfast  looke 

We  shall  discerne 
In  it,  as  in  some  holy  booke, 

How  man  may  heavenly  knowledge  learne. 

HABINGTON. 

THE  principles  on  which  spectrum  analysis  rests 
can  be  stated  so  concisely  that  I  shall  set  them 
forth  for  the  special  use  of  such  readers  as  may  not 
be  entirely  familiar  with  the  subject.    Every- 

Principles  J 

of  one  knows  that  when  the  rays  of  the  sun 

Spectrum  pass  through  a  triangular  prism  of  glass  or 
other  transparent  substance  they  are  un- 
equally refracted,  and  thus  separated  into  rays  of 
different  colours.  These  colours  are  not  distinct,  but 
each  runs  into  the  other  by  insensible  gradations,  from 
deep  crimson  through  red,  scarlet,  orange,  yellow, 
green,  and  blue  to  a  faint  violet! 

This  result  is  due  to  the  fact  that  the  light  of  the 
sun  is  made  up  of  an  indiscriminate  mixture  of  rays 

56 


SPEC  TR  UM  ANAL  YSIS  5 7 

of  an  infinite  number  of  wave-lengths,  or,  in  simpler 
language,  of  an  infinite  number  of  tints  of  colour, 
since  to  every  wave-length  corresponds  a  definite 
tint.  Such  a  spreading  out  of  elementary  colours 
in  the  form  of  a  visible  sheet  is  called  a  spectr^lm. 
By  the  spectrum  of  an  incandescent  object  is  meant 
the  spectrum  formed  by  the  light  emitted  by  the 
object  when  passed  through  a  refracting  prism  or 
otherwise  separated  into  its  elementary  colours.  The 
interest  and  value  which  attach  to  the  study  of  spectra 
arise  from  the  fact  that  different  bodies  give  different 
kinds  of  spectra,  according  to  their  constitution,  their 
temperature,  and  the  substances  of  which  they  are 
composed.  In  this  manner  it  is  possible,  by  a  study 
of  the  spectrum  of  a  body,  to  reach  certain  inferences 
respecting  its  constitution. 

In  order  that  such  a  study  should  lead  to  a  definite 
conclusion,  we  must  recall  that  to  each  special  shade 
of  colour  corresponds  a  definite  position  in  the  spec- 
trum. That  is  to  say,  there  is  a  special  kind  of  light 
having  a  certain  wave-length  and  therefore  a  certain 
shade  which  will  be  refracted  through  a  certain  fixed 
angle,  and  will  therefore  fall  into  a  definite  position 
in  the  spectrum.  This  position  is,  for  every  possible 
kind  of  light,  expressed  by  a  number  indicating  its 
wave-length. 

If  we  form  a  spectrum  with  the  light  emitted  by  an 
ordinary  incandescent  body,  a  gaslight  for  example, 
we  shall  find  the  series  of  colours  to  be  unbroken  from 
one  end  of  the  spectrum  to  the  other.  That  is  to 
say,  there  will  be  light  in  every  part  of  the  spectrum. 


58  THE  SPECTRA  OF  THE  STARS 

Such  a  spectrum  is  said  to  be  continuous.  But  if  we 
form  the  spectrum  by  means  of  sunlight,  we  shall 
find  the  spectrum  to  be  crossed  by  a  great  number  of 
more  or  less  dark  lines.  This  shows  that  in  the 
spectrum  of  the  sun  light  of  certain  definite  wave- 
lengths is  wholly  or  partly  wanting.  This  fact  has 
been  observed  for  more  than  a  century,  but  its  true 
significance  was  not  seen  until  a  comparatively  recent 
time. 

If,  instead  of  using  the  light  of  the  sun,  we  form  a 
spectrum  with  the  light  emitted  by  an  incandescent 
Spectrum  gas,  say  hydrogen  made  luminous  by  the 
Analysis,  electric  spark,  we  shall  find  that  the  spec- 
trum consists  only  of  a  limited  number  of  separate 
bright  lines,  of  various  colours.  This  shows  that 
such  a  gas,  instead  of  emitting  light  of  all  wave- 
lengths, as  an  incandescent  solid  body  does,  princi- 
pally emits  light  of  certain  definite  wave-lengths. 

It  is  also  found  that  if  we  pass  the  light  of  an  incan- 
descent body  through  a  sufficiently  large  mass  of  gas 
cooler  than  the  body,  the  spectrum,  instead  of  being 
entirely  continuous,  will  be  crossed  with  dark  lines 
like  that  of  the  sun.  This  shows  that  light  of  certain 
wave-lengths  is  absorbed  by  the  gas.  A  comparison 
of  these  dark  lines  with  the  bright  lines  emitted  by 
the  same  gas  when  incandescent  led  Kirchhoff  to  the 
discovery  of  the  following  fundamental  principle : 

Rvery  gas,  when  cold,  absorbs  the  same  rays  of  light 
which  it  emits  when  incandescent. 

An  immediate  inference  from  this  law  is  that  the 
dark  lines  seen  in  the  spectrum  of  the  sun  are  caused 


SPECTRUM  ANALYSIS 


59 


by  the  passage  of  the  light  through  gases  either  around 
the  sun  or  forming  the  atmosphere  of  the  earth.  A 
second  inference  is  that  we  can  determine  what  these 
gases  are  by  comparing  the  position  of  the  dark  lines 
with  that  of  the  bright  lines  produced  by  different 
gases  when  they  are  made  incandescent.  Hence 
arose  the  possibility  of  spectrum  analysis,  a  method 
which  has  been  applied  with  such  success  to  the 
study  of  the  heavenly  bodies. 

So  far  as  the  general  constitution  of  bodies  is  con- 
cerned, the  canons  of  spectrum  analysis  are  these  : 

Firstly,  when  a  spectrum  is  formed  of  distinct 
bright  lines,  the  light  which  forms  it  is  emitted  by  a 
transparent  mass  of  glowing  gas. 

Secondly,  when  a  spectrum  is  entirely  continuous 
the  light  emanates  either  from  an  incandescent  solid, 
from  a  body  composed  of  solid  particles,  which  may 
be  ever  so  small,  or  from  a  mass  of  incandescent  gas 
so  large  and  dense  as  not  to  be  transparent  through 
and  through. 

o 

Thirdly,  when  the  spectrum  is  continuous,  except 
that  it  is  crossed  by  fine  dark  lines,  the  body  emitting 
the  light  is  surrounded  by  an  atmosphere  formed  of 
gases  cooler  than  itself.  The  chemical  constitution 
of  these  gases  can  be  determined  by  the  position  of 
the  lines. 

Fourthly,  if,  as  is  frequently  the  case,  a  spectrum  is 
composed  of  an  irregular  succession  of  bright  and 
shaded  portions,  the  body  is  probably  a  gaseous  mass 
under  great  pressure. 

It  will  be  seen  from  the  preceding  statement  that 


60  THE  SPECTRA  OF  THE  STARS 

a  mass  of  gas  so  large  as  not  to  be  transparent  may 
not  be  distinguishable  from  a  solid  body.  It  is 
therefore  not  strictly  correct  to  say,  as  is  sometimes 
done,  that  an  incandescent  gas  always  gives  a  spec- 
trum of  bright  lines.  It  will  give  such  a  spectrum 
only  when  it  is  transparent  through  and  through.1 

A  gaseous  mass,  so  large  as  to  be  opaque,  would,  if 
it  were  of  the  same  temperature  inside  and  out,  give 
a  continuous  spectrum,  without  any  dark  lines.  But 
the  laws  of  temperature  in  such  a  mass  show  that  it 
will  be  cooler  at  the  surface  than  in  the  interior. 
This  cooler  envelope  will  absorb  the  rays  emanating 
from  the  interior,  as  in  the  case  when  the  latter  is 
solid.  We  conclude,  therefore,  that  the  fact  that  the 
great  majority  of  stars  show  a  spectrum  like  that 
of  the  sun,  namely,  a  continuous  one  crossed  by  dark 
lines,  does  not  throw  any  light  on  the  question 
whether  the  matter  composing  the  body  of  the  star  is 
in  a  solid,  liquid,  or  gaseous  state.  The  fact  is  that 
the  most  plausible  theories  of  the  constitution  of  the 
sun  lead  to  the  conclusion  that  its  interior  mass  is 
really  gaseous.  Only  the  photosphere  may  be  to 
a  greater  or  less  extent  solid  or  liquid.  The  dark 
lines  that  we  see  in  the  solar  spectrum  are  produced 

1  As  this  principle  is  not  universally  understood,  it  may  be  well  to  remark 
that  it  results  immediately  from  Kirchhoff's  law  of  the  proportionality  between 
the  radiating  and  absorbing  powers  of  all  bodies  for  light  of  each  separate 
wave-length.  When  a  body,  even  if  gaseous  in  form,  is  of  such  great  size  and 
density  that  light  of  no  colour  can  pass  entirely  through  it,  then  the  consequent 
absorption  by  the -body  of  light  of  all  colours  shows  that  throughout  the  region 
where  the  absorption  occurs  there  must  be  an  emission  of  light  of  these  same 
colours.  Thus  light  from  all  parts  of  the  spectrum  will  be  emitted  by  the 
entire  mass. 


DESCRIPTION  OF  THE  SPECTRUM  6r 

by  the  absorption  of  a  comparatively  thin  and  cool 
layer  of  gas  resting  upon  the  photosphere.  Analogy 
as  well  as  the  general  similarity  of  the  spectra  lead 
us  to  believe  that  the  constitution  of  most  of  the  stars 
is  similar  to  that  of  the  sun. 

The  visible  spectrum,  as  commonly  described,  term- 
inates with  the  red  at  one  end  and  the  violet  at  the 
other.  But  the  termination  is  by  no  means  Description 
sharp  at  either  end.  Especially  is  this  the  of  the 
case  with  the  violet,  where,  if  extraneous  light  sPectrum- 
be  shut  off,  a  faint  extension  known  as  the  ultra-violet, 
to  which  no  definite  limit  can  be  assigned,  will  become 
visible.  Moreover,  it  is  found  that  the  heating  effect 
does  not  terminate  with  the  red  end  of  the  spectrum, 
but  that  if  a  sensitive  thermometer  be  held  in  the 
seeming  darkness  beyond  the  red  end  a  heating  effect 
is  produced.  It  is  also  found  that  a  photographic 
effect  is  produced  by  rays  scarcely,  if  at  all,  visible  in 
the  ultra-violet. 

These  three  different  effects  w.ere  formerly  at- 
tributed to  three  different  kinds  of  rays,  those  of 
heat,  those  of  light,  and  those  which,  affecting  the 
photographic  plate,  were  called  chemical  or  actinic 
rays.  But  it  is  now  known  that  heat,  light,  and  pho- 
tographic effects  are  all  due  to  one  and  the  same 
agency,  which  we  may  call  radiance.  The  radiance 
from  an  incandescent  body  like  the  sun  may  be  of 
all  wave-lengths  ;  at  least  we  can  set  no  definite  limit 
to  the  wave-length.  These  lengths  may  be  expressed 
in  millionths  of  a  millimetre,  or,  as  is  now  more 
commonly  done,  in  ten  millionths.  This  measure  is 


62  THE  SPECTRA  OF  THE  STARS 

sometimes  called  the  tenth-metre,  meaning  the  metre 
divided  by  the  tenth  power  of  ten.  To  give  a  general 
idea  of  wave-length  we  remark  that  near  the  brightest 
part  of  the  spectrum  the  wave-length  is  5000  tenth- 
metres  or  500  millionths  of  a  millimetre,  the  latter 
being  nearly  ^  of  our  inch.  The  wave-length  in 
question  is  therefore  about  y^-j-^  of  an  inch.  As  we 
pass  toward  the  violet  end  of  the  spectrum,  commonly 
called  the  upper  end,  this  wave-length  diminishes  ;  as 
we  pass  toward  the  lower  or  red  end  it  increases.  As 
we  approach  wave-length  7500,  the  effect  on  the  eye 
as  light  gradually  dies  away  with  a  sensation  of  very 
deep  red  ;  below  that  point  only  the  heat  effect  is 
produced,  except  that  with  certain  chemicals  a  faint 
photographic  effect  may  still  be  obtained. 

The  more  refrangible  parts  of  the  spectrum  are  now 
studied  almost  entirely  by  photography.  The  astro- 
physicist can  photograph  not  only  the  visible  spec- 
trum at  pleasure,  but  the  higher  parts  of  the  spectra 
of  bodies  even  when  so  faint  as  to  be  invisible  to  the 
eye.  The  photograph  has  the  additional  advantage 
that  it  forms  a  permanent  record  which  can  be 
measured  and  studied  at  pleasure. 

The  farthest  exploration  into  the  ultra-violet  region 
has  been  made  by  Dr.  V.  Schumann,  who  has  exam- 
ined it  up  to  W.  L.  1620.  The  higher  region  is  very 
rich  in  lines,  of  which  he  found  more  than  six  hundred, 
separated  into  fifteen  groups.  As  we  approach  its 
limit  the  air  becomes  opaque  to  radiation.  A  layer 
of  one  millimetre  in  thickness  was  found  to  absorb  all 
the  radiance  shorter  than  1 700. 


DESCRIPTION  OF   THE  SPECTRUM  63 

The  strongest  dark  lines  of  the  spectra  were  studied 
by  Wollaston  in  1802.  Later  Fraunhofer  designated 
the  strongest  by  the  capital  letters  A,  B,  C,  D, 
E,  and  F,  to  which  some  small  letters  were  subse- 
quently added.  As  the  exploration  of  the  spectrum 
extended  into  the  violet  additional  letters  were  added. 
It  has  been  found  convenient  in  recent  times  to  re- 
place some  of  those  letters  by  symbols  expressing  the 
substance  which  produces  the  line.  Thus,  the  line 
called  by  Fraunhofer  C,  being  produced  by  hydro- 
gen, is  now  frequently  called  H«.  The  other  lines 
produced  by  this  substance  are  designated  as  H/s, 
Hr,  etc. 

Extensive  maps  of  the  solar  spectrum  have  been 
published,  of  which  that  of  Rowland  surpasses  all  others 
in  the  completeness  of  its  details.  The  number  of  spec- 
tral lines  as  found  on  this  map  mount  high  into  the 
thousands,  so  that  the  great  mass  of  them  can  be  desig- 
nated only  by  their  wave-length.  Thus  the  line  C  or 
Ha  may  be  designated  as  6561.7.  Maps  or  tables  of 
the  spectra  of  the  various  chemical  elements  are  found 
in  special  treaties  on  the  subject. 

While  some  substances,  notably  the  lightest  and 
most  permanent  gases,  have  few  lines  in  their  respect- 
ive spectra,  in  other  substances  the  lines  are  very  nu- 
merous. The  metal  which  gives  the  richest  spectrum 
is  iron.  Thalen  has  recorded  not  less  than  1200  lines 
in  its  spectrum  between  wave-lengths  4000  and  7600. 

It  is  now  found  that  the  spectra  of  most  substances 
vary  with  the  physical  condition  of  the  substance  in 
such  a  way  that  detection  may  become  doubtful  or 


64  THE  SPECTRA  OF  THE  STARS 

difficult.  The  general  rule  is  that,  when  a  gas  is  sub- 
jected to  pressure,  the  lines,  if  dark,  become  blacker 
and  broader,  being  sometimes  changed  into  bands 
with  more  or  less  ill-defined  borders.  Commonly  the 
line  broadens  only  on  one  side,  thus  leading  to  a 
displacement  of  its  apparent  position  with  the  press- 
ure. Not  less  than  three  distinct  spectra  have  been 
found  as  due  to  argon.  These  changes  have  not, 
up  to  the  present  time,  been  expressed  by  any  uni- 
form and  general  law.  It  is  not  alone  the  thickness 
of  the  lines  which  changes ;  it  frequently  happens 
that  a  line  visible  under  one  condition  will  disappear 
under  another,  while  a  second  will  be  better  seen. 
These  seeming  anomalies  may  sometimes  make  our 
conclusions  from  the  spectral  analysis  of  the  heavenly 
bodies  uncertain ;  but  it  may  be  hoped  that  when 
they  are  fully  understood,  they  will  give  us  more 
precise,  knowledge  than  we  yet  possess  of  the  exact 
physical  constitution  of  these  bodies. 

A  complete  map  of  the  spectrum  is  too  full  of 
detail  to  well  serve  the  purpose  of  the  general  reader 
or  student.  We  therefore  give  on  the  opposite  page 
a  plan  of  the  visible  spectrum,  giving  the  wave- 
lengths, the  arrangement  of  colours,  and  a  few  of  the 
stronger  lines  with  the  substances  to  which  they  are 
due.  It  must  not,  however,  be  supposed  that  the  solar 
spectrum  with  its  lines  is  so  simple  as  might  appear 
from  this  plan.  For  the  most  part,  what  are  drawn 
and  lettered  as  lines  really  consist  of  groups  of  lines 
of  different  degrees  of  intensity.  Whether  they  shall 
appear  as  a  simple  ill-defined  line  or  a  group  depends 


PLAN  OF  THE  SPECTRUM 


WAVE 
LENGTH 

j^son  ••  -i 

LINE  AND  DESIGNATION 

SUBSTANCE. 

OR  ORIGIN 

N 

37  

ULTRA    VIOLET 
M 

38 

39  

K-u-  — 

CALCIUM 

4OOO  — 

Hor  hfc  
h  or  Hf 

CALCIUM.  HYDROGEN 
HVDROGEN 

42  
43  

VIOLET 

--a-u  

IRON 

44  
4500- 
46  
47  
48  

Hy  

BLUE 

^_                   For  Hfi 

HYDROGEN 

49  

NEBULAR  LINE 

5000— 

NEBULAR  LINE 

51  

GREEN 

MAGNESIUM 

52 

E 

CALCIUM 

53  
54  
5500- 
56  
57  1 
58  ] 

GREENISH  YELLOW 

YELLOW 

PI  n> 

SODIUM 

6OOO- 
61  
62  
63  
64  
650O- 

ORANGE. 
SCARLET 

C  or  Htf         '      -B  «  -*~ 

HYDROfiFN 

66  
67  
66  

BRIGHT  RED 

B 

AQUEOUS  VAPOR 

69  

7000— 
71  
•70 

DEEP  RED 

AQUEOUS  VAPOR 

73  
74  
7500- 
yc 

PARK  RED 

A 

i 

AQUEOUS  VAPOR 

65 


66  THE  SPECTRA  OF  THE  STARS 

largely  on  the  resolving  power  of  the  spectroscope. 
With  every  increase  of  power  new  lines  are  brought 
out.  It  will  also  be  seen  from  the  photographs 
which  we  reproduce  that  the  spectra  of  the  heavenly 
bodies,  whether  stars  or  sun,  do  not  consist  of  uni- 
form sheets  of  light  crossed  by  dark  lines,  but  that 
one  part  runs  into  another  with  slight  and  nearly 
imperceptible  gradations  of  shade.  These  are  due 
partly  to  innumerable  lines  not  visible  singly,  and 
partly  to  the  varying  and  irregular  absorption  to 
which  the  light  has  been  subject. 

Particularly  irregular  is  the  absorption  produced  by 
the  aqueous  vapour  of  the  atmosphere.  The  strong- 
est lines  and  groups  of  lines  in  the  red,  notably  those 
between  A  and  B,  as  well  as  irregular  shadings  in  the 
bright  parts  of  the  spectrum,  are  due  to  the  absorp- 
tion of  this  agent. 

It  thus  happens  that  the  individual  Wollaston  lines 
cannot  as  a  general  rule  be  considered  as  each  due 
to  some  one  substance,  most  of  them  being  composed 
of  a  number  of  lines  produced  by  different  substances 
whose  lines  chance  to  fall  very  close  together. 

In  connection  with  the  lines  and  the  wave-lengths 
we  have  also  named  the  spectral  colours.  One  of 
these  shades  into  the  other  so  gradually  that  no  pre- 
cise line  of  demarkation  can  be  drawn.  In  fact,  the 
change  of  colour  is  continuous  from  one  end  of  the 
spectrum  to  the  other.  The  red,  green,  blue,  and 
violet  are  the  only  colours  which,  to  the  eye,  seem 
unchanged  through  any  perceptible  space  in  their 
central  portions. 


CLASSIFICATION  OF  STELLAR  SPECTRA       67 

Different  authorities,  and  perhaps  different  eyes, 
may  therefore  assign  different  boundaries  to  the  col- 
ours. For  these  reasons  we  have  not  attempted  to 
draw  any  demarkations  of  the  colours,  but  have  simply 
shown  the  central  parts  of  those  colours  which  are 
best  marked. 

Quite  possibly  different  eyes  may  have  slightly 
different  impressions  of  the  spectral  colours.  To  those 
of  the  writer,  the  yellow  of  the  spectrum  is  in  no  way 
comparable  in  depth  and  intensity  with  the  yellow  of 
such  flowers  as  the  buttercup.  The  shading  from  a 
tinge  of  red  on  the  one  side  to  a  tinge  of  green  on 
the  other  takes  place  without  what  seems  like  a  pure 
bright  yellow. 

When  the  spectra  of  thousands  of  stars  were  re- 
corded for  study,  such  a  variety  was  found  that  some 
system  of  classification  was  necessary.     The 
commencement  of  such  a  system  was  made         tion  of 
by  Secchi  in    1863.      It  was  based   on  the        Stellar 
observed  relation  between  the  colour  of  a 
star    and    the    general    character   of    its    spectrum. 

Arranging  the  stars  in  a  regular  series,  from  blue 
in  tint  through  white  to  red,  it  was  found  that  the 
number  and  character  of  the  spectral  lines  varied  in  a 
corresponding  way.  The  blue  stars,  like  Sirius,  Vega, 
and  Alpha  Aquilse,  had  the  F  lines  strong,  as  well  as 
the  two  violet  lines  H,  but  had  otherwise  only  ex- 
tremely fine  lines.  On  the  other  hand,  the  red  stars, 
like  Alpha  Orionis  and  Alpha  Scorpii,  show  spectra 
with  several  broad  bands.  Secchi  was  thus  led  to 
recognise  three  types  of  spectra,  as  follows  : 


Type  II 
EXAMPLES  OF  STELLAR  SPECTRA 


Type  II 


CLASSIFICATION  OF  STELLAR  SPECTRA       69 

The  first  type  is  that  of  the  white  or  slightly  blue 
stars,  like  Sirius,  Vega,  Altair,  Rigel,  etc.  The  typi- 
cal spectrum  of  these  stars  shows  all  seven  spectral 
colours,  interrupted  by  four  strong,  dark  lines,  one  in 
the  red,  one  in  the  bluish  green,  and  the  two  others 
in  the  violet.  All  four  of  these  lines  belong  to  hy- 
drogen. Their  marked  peculiarity  is  their  breadth, 
which  shows  that  the  absorbing  layer  is  of  consider- 
able thickness,  or  is  subjected  to  a  great  pressure. 
Besides  these  broad  rays,  fine  metallic  rays  are  found 
in  the  brighter  stars  of  this  type.  Secchi  considers 
that  this  is  the  most  numerous  type  of  all,  half  the 
stars  which  he  studied  belonging  to  it. 

The  second  type  is  that  of  the  somewhat  yellow 
stars,  like  Capella,  Pollux,  Arcturu.s,  Procyon,  etc. 
The  most  striking  feature  of  the  spectrum  of  these 
stars  is  its  resemblance  to  that  of  our  sun.  Like  the 
latter,  it  is  crossed  by  very  fine  and  close  black  rays. 
It  would  seem  that  the  more  the  star  inclines  toward 
red,  the  broader  these  rays  become  and  the  easier  it 
is  to  distinguish  them.  We  give  a  figure  showing 
the  remarkable  agreement  between  the  spectrum  of 
Capella,  which  may  be  taken  as  an  example  of  the 
type,  and  that  of  the  sun. 

The  spectra  of  the  third  type,  belonging  mostly  to 
the  red  stars,  are  composed  of  a  double  system  of 
nebulous  bands  and  dark  lines.  The  latter  are  funda- 
mentally the  same  as  in  the  second  type,  the  broad, 
nebulous  bands  being  an  addition  to  the  spectrum. 
Alpha  Herculis  may  be  taken  as  an  example  of  this 
type. 


7o  THE  SPECTRA  OF  THE  STARS 

It  is  to  be  remarked  that,  in  these  progressive 
types,  the  brilliancy  of  the  more  refrangible  end  of 
the  spectrum  continually  diminishes  relatively  to  that 
of  the  red  end.  To  this  is  due  the  gradations  of 
colour  in  the  stars. 

To  these  three  types  Secchi  subsequently  added  a 
fourth,  given  by  a  comparatively  few  stars  of  a  deep 
red  colour.  The  spectra  of  this  class  consist  princi- 
pally of  three  bright  bands,  which  are  separated  by 
dark  intervals.  The  brightest  is  in  the  green  ;  a  very 
faint  one  is  in  the  blue ;  the  third  is  in  the  yel- 
low and  red,  and  is  divided  up  into  a  number  of 
others. 

To  these  types  a  fifth  v/as  subsequently  added  by 
Wolf  and  Rayet,  of  the  Paris  Observatory.  The 
spectra  of  this  class  show  a  singular  mixture  of  bright 
lines  and  dark  bands,  as  if  three  different  spectra 
were  combined,  one  continuous,  one  an  absorption 
spectrum,  and  one  an  emission  spectrum  from  glowing 
gas.  Less  than  a  hundred  stars  of  this  type  have 
been  discovered.  A  very  remarkable  peculiarity, 
which  we  shall  discuss  hereafter,  is  that  they  are 
nearly  all  situated  very  near  the  central  line  of  the 
Milky  Way. 

Vogel  proposed  a  modification  of  Secchi's  classi- 
fication, by  subdividing  each  of  his  three  types  into 
two  or  three  others,  and  including  the  Wolf-Rayet 
stars  under  the  second  type.  His  definitions  are  as 
follows  : 

Type  I  is  distinguished  by  the  intensity  of  the 
light  in  the  more  refrangible  end  of  the  spectrum,  the 


CLASSIFICATION  OF  STELLAR  SPECTRA       71 

blue  and  violet.  The  type  may  be  divided  into  three 
subdivisions,  designated  a,  b,  and  c  : 

In  \a  the  metallic  lines  are  very  faint,  while  the 
hydrogen  lines  are  distinguished  by  their  breadth  and 
strength. 

In  \b  the  hydrogen  lines  are  wanting. 

In  If  the  lines  of  hydrogen  and  helium  both  show 
as  bright  lines.  Stars  showing  this  spectrum  are  now 
known  as  helium  stars. 

According  to  Vogel,  the  spectra  of  type  II  are  dis- 
tinguished by  having  the  metallic  lines  well  marked 
and  the  more  refrangible  end  of  the  spectrum  much 
fainter  than  in  the  case  of  type  I.  He  recognises  two 
subdivisions  : 

In  lla  the  metallic  lines  are  very  numerous,  es- 
pecially in  the  yellow  and  green.  The  hydrogen 
lines  are  strong,  but  not  so  striking  as  in  la. 

In  lib  are  found  dark  lines,  bright  lines,  and  faint 
bands.  In  this  subdivision  he  includes  the  Wolf- 
Rayet  stars,  more  generally  classified  as  of  the  fifth 
type. 

The  distinguishing  mark  of  the  third  type  is  that, 
besides  dark  lines,  there  are  numerous  dark  bands  in 
all  parts  of  the  spectrum,  and  the  more  refrangible 
end  of  the  latter  is  almost  wanting.  There  are  two 
subdivisions  of  this  type  : 

In  Ilia  the  broad  bands  nearest  the  violet  end  are 
sharp,  dark,  and  well  defined,  while  those  near  the  red 
end  are  ill  defined  and  faint.  In  1116  the  bands  near 
the  red  end  are  sharp  and  well  defined  ;  those  toward 
the  violet,  faint  and  ill  defined.  The  character  of  the 


7  2  THE  SPECTRA  OF  THE  STARS 

bands  is  therefore  the  reverse  of  that  in  subdivi- 
sion a. 

This  classification  of  Vogel  is  still  generally  followed 
in  Germany  and  elsewhere.  It  is  found,  however, 
that  there  are  star  spectra  of  types  intermediate  to  all 
these  defined.  Moreover,  in  each  type  the  individual 
differences  are  so  considerable  that  there  is  no  well- 
defined  limit  to  the  number  of  classes  that  may  be 
recognised.  Other  designations  frequently  occur  in 
literature.  The  stars  of  type  II  are  sometimes 
termed  Capellan  stars,  or  solar  stars.  The  stars 
which  show  the  lines  of  helium  are  known  as  helium 
stars. 

A  classification  far  more  minute  than  either  of  the 
preceding  was  made  by  Miss  Antonio  C.  Maury,  of 
the  Harvard  Observatory,  and  has  been  adopted  in 
the  Draper  Memorial  work  of  that  institution.1  The 
classification  is  too  extended  for  us  to  give  more  than 
its  principal  features.  In  the  main  it  recognises  a 
regular  progression  in  the  character  of  the  spectra. 
The  principal  feature  is  the  addition  of  an  extended 
type  called  the  Orion  type,  because  the  stars  show- 
ing it  abound  in  the  constellation  Orion,  though  not 
confined  to  it.  It  is  marked  principally  by  what  are 
called  Orion  lines,  which  include  most  of  the  lines  of 
hydrogen,  and  nearly  one  hundred  others.  Few  or 
none  of  the  latter  can  be  recognised  as  solar  lines, 
nor  can  they  certainly  be  ascribed  to  any  known  sub- 
stances. The  peculiar  feature  of  the  type  is  that  the 
Orion  lines  are  strong  and  numerous,  declining  in  the 

1  Annals  Harvard  Observatory,  vol.  xxviii.,  No.  I. 


.RESULTS  OF  SPECTRUM  ANALYSIS 


73 


later  groups.  The  hydrogen  lines  are  of  moderate 
intensity,  inclining  toward  those  of  the  first  type.  Of 
the  two  main  calcium  lines,  K  is  often,  and  H  gener- 
ally, absent. 

This  Orion  type  is  divided  into  five  groups :  type 
I  into  five,  types  II  and  III  each  into  four.  Besides 
these  there  are  several  intermediate  groups,  and 
a  group  each  for  the  fourth  and  fifth  types,  the 
whole  number  of  such  groups  being  twenty-two. 
Each  group  is  still  further  subdivided  into  classes. 

There  are  many  star  spectra  which  cannot  be  in- 
cluded in  any  of  the  classes  we  have  described.  Up 
to  the  present  time  these  are  generally  described  as 
stars  of  peculiar  spectra. 

As  the  present  chapter  is  confined  to  the  more 
general  side  of  the  subject,  we  shall  not  attempt  any 
description  of  special  spectra.  These,  especially  the 
peculiar  spectra  of  the  nebulae,  of  new  stars,  of  vari- 
able stars,  etc.,  will  be  referred  to,  so  far  as  necessary, 
in  the  chapters  relating  to  those  objects. 

The  most  interesting  conclusion  drawn  from  ob- 
servations with  the  spectroscope  is  that  the  stars  are 
composed,  in  the  main,  of  elements  similar  Resuits  of 
to  those  found  in  our  sun.  As  the  latter  Spectrum 
contains  most  of  the  elements  found  on  the  Analysis- 
earth  and  few  or  no  others,  we  may  say  that  earth 
and  stars  seem  to  be  all  made  out  of  like  matter. 
It  is,  however,  not  yet  easy  to  decide  to  what  extent 
elements  unknown  on  the  earth  exist  in  the  heavens. 
It  would  scarcely  be  safe  to  assume  that,  because 
the  line  of  some  terrestial  substance  is  found  in  the 


74  THE  SPECTRA  OF  THE  STARS 

spectrum  of  a  star,  it  is  produced  by  that  substance. 
It  is  quite  possible  that  an  unknown  substance  might 
show  a  line  in  appreciably  the  same  position  as  that 
of  some  substance  known  to  us.  The  evidence  be- 
comes conclusive  only  in  the  case  of  those  elements 
of  which  the  spectral  lines  are  so  numerous  that  when 
they  all  coincide  with  lines  given  by  a  star  there  can 
be  no  doubt  of  the  identity. 


CHAPTER  VI 
PROPER  MOTIONS  OF  THE  STARS 

I  'm  constant  as  the  Northern  Star, 

Of  whose  true-fixed  and  vesting  quality 

There  is  no  fellow  in  the  firmament. — SHAKESPEARE. 

WE  may  assume  that  the  stars  are  all  in  motion. 
It  is  true  that  only  a  comparatively  small 
number  of  stars  have  been  actually  seen  to  be  in 
motion ;  but  as  some  motion  exists  in  nearly  every 
case  where  observations  would  permit  of  its  being  de- 
termined, we  may  assume  the  rule  to  be  universal. 
Moreover,  if  a  star  were  at  rest  at  any  time  it  would 
be  set  in  motion  by  the  attraction  of  other  stars. 

In  dealing  with  the  subject,  the  astronomer  com- 
monly expresses  the  motion  in  angular  measurement, 
as  so  many  seconds  per  year  or  per  century.  The 
keenest  eye  would  not,  without  telescopic  aid,  be  able 
to  distinguish  between  two  stars  whose  apparent  dis- 
tance is  less  than  2'  or  120"  of  arc.  The  pair  of  stars 
known  as  Epsilon  Lyrse  are  over  3'  apart ;  yet  to  ord- 
inary vision  they  appear  as  a  single  star.  To  ap- 
preciate what  i"  of  arc  means  we  must  conceive  that 
the  distance  between  these  two  stars  is  divided  by 
200.  Yet  this  minute  space  is  easily  distinguished 
and  accurately  measured  by  the  aid  of  a  telescope  of 
ordinary  power. 

75 


76  PROPER  MOTIONS  OF  THE  STARS 

Statements  of  the  motion  from  different  points  of 
view  illustrate  in  a  striking  way  the  vast  distance  of 
Apparent  tne  stars  an^  tne  power  of  modern  telescopic 
and  Real  research.  If  Hipparchus  or  Ptolemy  should 
Motions.  rjse  from  hjs  sleep  of  two  thousand  years 

—  nay,  if  the  earliest  priests  of  Babylon  should  come 
to  life  again  and  view  the  heavens,  they  would  not 
perceive  any  change  to  have  taken  place  in  the  relat- 
ive positions  of  the  stars.  The  general  configurations 
of  the  constellations  would  be  exactly  that  to  which 
they  were  accustomed.  Had  they  been  exact  ob- 
servers they-  might  notice  a  slight  change  in  the 
position  of  Arcturus;  but  not  in  that  of  any  other  star. 

Slow  as  the  angular  motion  is,  our  telescopic 
power  in  the  course  of  a  few  years  makes  its  detection 
frequently  possible — in  the  case  of  Arcturus  even  in  a 
few  weeks.  As  accurate  determinations  of  posi- 
tions of  the  stars  have  been  made  only  during  a 
century  and  a  half,  no  motions  can  be  positively 
determined  except  those  which  would  become  evi- 
dent to  telescopic  vision  in  that  period.  Only 
about  three  thousand  stars  have  been  accurately  ob- 
served so  long  as  this.  In  the  large  majority  of  cases 
the  interval  of  observation  is  so  short  or  the  motion 
so  slow  that  nothing  can  be  asserted  respecting  the 
law  of  the  motion. 

Contrast  these  apparently  slow  motions  with  the 
actual  motions.  Swift  indeed  are  these  when  meas. 
ured  by  terrestrial  standards.  Arcturus  has  been 
moving  ever  since  the  time  of  Job  at  the  rate  of 
probably  more  than  two  hundred  miles  per  second— 


APPARENT  AND  REAL  MOTIONS  77 

possibly  three  hundred  miles.  Generally,  however, 
the  motion  is  much  smaller,  ranging  from  an  imper- 
ceptible quantity  up  to  forty  miles  a  second. 

The  great  mass  of  stars  seem  to  move  only  a  few 
seconds  per  century,  but  there  are  some  whose  mo- 
tions are  exceptionally  rapid.  The  general  rule  is 
that  the  brighter  stars  have  the  largest  proper  motions. 
This  is  what  we  should  expect,  because  in  the  gen- 
eral average  they  are  nearer  to  us,  and  therefore  their 
motion  will  subtend  the  greatest  angle  to  the  eye. 
But  this  rule  is  only  one  of  majorities.  As  a  matter 
of  fact,  the  stars  of  largest  proper  motion  happen  to 
be  low  in  the  scale  of  magnitude.  It  happens  thus 
because  the  number  of  stars  of  smaller  magnitudes 
is  so  much  greater  than  that  of  the  brighter  ones 
that  their  very  small  proportion  of  large  proper 
motions  exceeds  in  actual  number  those  among  the 
brighter  stars. 

The  discovery  of  the  star  of  greatest  known  proper 
motion  was  made  by  Kapteyn,  of  Groningen,  in  1897, 
co-operating  with  Gill  and  Innes,  of  the  Cape  Ob- 
servatory. While  examining  the  photographs  of  the 
stars  made  at  this  institution,  Kapteyn  was  surprised 
to  notice  the  impression  of  a  star  of  the  eighth  magni- 
tude which  at  first  could  not  be  found  in  any  cata- 
logue. But  on  comparing  different  star  lists  and 
different  photographs  it  soon  became  evident  that  the 
star  had  been  previously  seen  or  photographed,  but 
always  in  different  positions.  An  examination  of  the 
observed  positions  at  various  times  showed  that  the 
star  had  a  more  rapid  proper  motion  than  any  other 


PROPER  MOTIONS  OF  THE  STARS 


yet  known.  Yet,  great  though  this  motion  is,  it  would 
require  nearly  150,000  years  for  the  star  to  make  a 
complete  circuit  of  the  heavens  if  it  moved  round  the 
sun  uniformly  at  its  present  rate. 

The  following  is  a  list  of  the  annual  proper  mo- 
tions of  nine  stars  exceeding  4".  We  add  the  po- 
sitions and  magnitudes  of  the  stars. 


STAR 

POSITION 

MAG. 

PROP. 
MOT. 

R.  A. 

DEC. 

Z   C   «;h   241 

h 

5 
II 

.22 
O 
21 
IO 
21 
II 

4 

m 
7 
47 
5<J 
O 
2 
5« 

5'' 

O 

ix 

--45-  0 
+38.4 
-36.4 
-37-3 
+38-2 
+44-3 
-57-2 
+44-0 
-  7.8 

8-5 
6.4 

8.1 
4-8 
7-3 
4.8 
8.7 
4-5 

8.70 
7.04 

7.00 
6.07 

5.20 
4.76 
4.68 
4.41 
4.06 

Lacaille  9352            

Cord   32416    

Ll.  21  185    

e  Indi  

Ll.  21  258  

o2  Eridani 

The  fact  that  the  stars  move  suggests  a  very  nat- 
ural analogy  to  the  solar  system.  In  the  latter  a 
Moving  number  of  planets  revolve  round  the  sun 
Systems  as  their  centre,  each  planet  continually  de- 

stars'  scribing  the  same  orbit,  while  the  various 
planets  have  different  velocities.  Around  several  of 
the  planets  revolve  one  or  more  satellites.  Were 
civilised  men  ephemeral,  observing  the  planets  and 
satellites  only  for  a  few  minutes,  these  bodies  would 
be  described  as  having  proper  motions  of  their  own, 
as  we  find  the  stars  to  have.  May  it  not  then  be 
that  the  stars  also  form  a  system  ;  that  each  star 
is  moving  in  a  fixed  orbit,  performing  a  revolution 
around  some  far-distant  centre  in  a  period  which  ma> 


MOVING  SYSTEMS  OF  STARS  79 

be  hundreds  of  thousands  or  hundreds  of  millions  of 
years  ?  May  it  not  be  that  there  are  systems  of  stars 
in  which  each  star  revolves  around  a  centre  of  its  own 
while  all  these  systems  are  in  revolution  around  a 
single  centre  ? 

This  thought  has  been  entertained  by  more  than 
one  contemplative  astronomer.  Lambert's  magnifi- 
cent conception  of  system  upon  system  will  be 
described  hereafter.  Madler  thought  that  he  had 
obtained  evidence  of  the  revolution  of  the  stars 
around  Alcyone,  the  brightest  of  the  Pleiades,  as 
a  centre.  But,  as  the  proper  motions  of  the  stars 
are  more  carefully  studied  and  their  motion  and 
direction  more  exactly  ascertained,  it  becomes  very 
clear  that  when  considered  on  a  large  scale  these  con- 
ceptions are  never  realised  in  the  actual  universe  as  a 
whole.  But  there  are  isolated  cases  of  systems  of 
stars  which  are  shown  to  be  in  some  way  connected 
by  their  having  a  common  proper  motion.  We  shall 
mention  some  of  the  more  notable  cases. 

The  Pleiades  are  found  to  move  together  with  such 
exactness  that  up  to  the  present  time  no  difference  in 
their  proper  motions  has  been  detected.  This  is  true 
not  only  of  the  six  stars  which  we  readily  see  with 
the  naked  eye,  but  of  a  much  larger  number  of  fainter 
ones  made  known  by  the  telescope.  It  is  an  interest- 
ing fact,  however,  that  a  few  stars  apparently  within 
the  group  do  not  partake  of  this  motion,  from  which 
it  may  be  inferred  that  they  do  not  belong  to  the 
system.  But  there  must  be  some  motion  among 
themselves,  else  the  stars  would  ultimately  fall  to- 


8o  PROPER  MOTIONS  OF  THE  STARS 

gether  by  their  mutual  attraction.  The  amount  and 
nature  of  this  motion  cannot,  however,  be  ascertained 
except  by  centuries  of  observation. 

Another  example  of  the  same  sort  is  seen  in  five 
out  of  the  seven  stars  of  Ursa  Major,  or  The  Dipper. 
The  stars  are  those  lettered  ft,  y,  3,  f,  and  0.  All  five 
have  a  proper  motion  in  R.  A.  of  nearly  8"  per  cent- 
ury, while  in  declination  the  movements  are  some- 
times positive  and  sometimes  negative ;  that  is  to 
say,  some  of  the  stars  are  lessening  their  distance 
from  the  pole,  while  others  are  increasing  it.  But 
when  we  project  the  motions  on  a  map  we  find 
that  the  actual  direction  is  very  nearly  the  same  for 
all  five  stars,  and  the  reason  why  some  move  slightly 
to  the  north  and  others  slightly  to  the  south  is  due  to 
the  divergence  of  the  circles  of  right  ascension.  It  is 
worthy  of  remark  that  the  community  of  motion  is 
also  shown  by  spectroscopic  observations  of  the 
radial  motions  described  below. 

The  five  stars  in  question  are  all  of  the  second 
magnitude  except  Delta,  which  is  of  the  third.  It  is 
a  curious  fact  that  no  fainter  stars  than  these  five 
have  been  found  to  belong  to  the  system. 

From  a  study  of  these  motions  Hoffler  has  con- 
cluded that  the  five  stars  lie  nearly  in  the  same  plane 
and  have  an  equal  motion  in  one  and  the  same  direc- 
tion. From  this  hypothesis  he  has  made  a  determin- 
ation of  their  relative  and  actual  distances.  The 
result  reached  in  this  way  cannot  yet,  however,  be 
regarded  as  conclusive. 

There  are  three  stars  in  Cassiopeia,  Beta,  Eta,  and 


RADIAL  MOTIONS  OF  THE  STARS  81 

Mu,  each  having  a  large  proper  motion  in  so  nearly 
the  same  direction  that  it  is  difficult  to  avoid  at  least 
a  suspicion  of  some  relation  between  them.  The 
angular  motions  are,  however,  so  far  from  equal  that 
we  cannot  regard  the  relation  as  established. 

In  the  constellation  Taurus,  between  Aldebaran 
and  the  Pleiades,  most  of  the  stars  which  have  been 
accurately  determined  seem  to  have  a  motion  which 
is  positive  in  R.  A.  and  negative  in  declination.  But 
these  motions  are  not  equal,  as  they  should  be  if  the 
stars  belonged  to  one  system,  and  we  cannot  draw  any 
definite  conclusion  from  them.  They  show  a  phenom- 
enon which  Proctor  very  aptly  designated  as  star-drift. 

Another  curious  case  is  that  of  A  Ophiuchi  and  a 
smaller  star  of  the  seventh  magnitude,  about  14'  from 
it,  having  an  equal  proper  motion,  showing  the  two 
to  form  a  connected  system. 

The  systems  we  have  just  described  comprise  stars 
situated  so  far  apart  that,  but  for  their  common  mo- 
tion, we  should  not  have  suspected  any  relation  be- 
tween them.  The  community  of  origin  which  their 
connection  indicates  is  of  great  interest  and  import- 
ance, but  this  subject  belongs  to  a  later  chapter. 

No  achievement  of  modern  science  is  more  remark- 
able than  the  measurement  of  the  velocity  with  which 
stars  are  moving  to  or  from  us.  This  is  ef- 

8  Radial 

fected  by  means  ot  the  spectroscope  through      Motions 
a  comparison  of  the  position  of  the  spectral          of  the 
lines  produced  by  the  absorption  of  any  sub- 
stance in  the  atmosphere  of  the  star  with  the  corre- 
sponding lines  produced  by  the  same  substance  on 


82  PROPER  MOTIONS  OF  THE  STARS 

the  earth.  The  principle  on  which  the  method  de- 
pends may  be  illustrated  by  the  analogous  case  of 
sound.  It  is  a  familiar  fact  that  if  we  stand  alongside 
a  railway  while  a  locomotive  is  passing  us  at  full 
speed  and  at  the  same  time  blowing  a  whistle,  the 
pitch  of  the  note  which  we  hear  from  the  whistle  is 
higher  as  the  engine  is  approaching  than  after  it 
passes.  The  reason  is  that  the  pitch  of  a  sound  de- 
pends upon  the  number  of  sound-beats  per  second. 

Now,  we  may  consider  the  waves  which  form  light, 
when  they  strike  our  apparatus,  as  beats  in  the  ethe- 
real medium  which  follow  each  other  with  extraordin- 
ary rapidity,  millions  of  millions  in  a  second,  moving 
forward  with  a  definite  velocity  of  more  than  186,000 
miles  a  second.  Each  spectral  line  produced  by  a 
chemical  element  shows  that  that  element,  when  in- 
candescent, beats  the  ether  a  certain  number  of  times 
in  a  second.  These  beats  are  transmitted  as  waves. 
Since  the  velocity  is  the  same  whether  the  number  of 
beats  per  second  is  less  or  greater,  it  follows  that,  if 
the  body  is  in  motion  in  the  direction  in  which  it 
emits  the  light,  the  beats  will  be  closer  together  than  if 
it  is  at  rest ;  if  moving  away  they  will  be  farther  apart. 
The  fundamental  fact  on  which  this  result  depends  is 
that  the  velocity  of  the  light-beat  through  the  ether 
is  independent  of  the  motion  of  the  body  causing  the 

A        B  X 

0 


beat.     To  show  the  result,  let  A  be  a  luminous  body 


RADIAL  MOTIONS  OF  THE  STARS  83 

at  rest ;  let  the  seven  dots  to  the  right  of  A  be  the 
crests  of  seven  waves  or  beats,  the  first  of  which,  at 
the  end  of  a  certain  time,  has  reached  X.  The  wave- 
length will  then  be  one-seventh  the  distance  A  X. 
Now,  suppose  A  in  motion  toward  X  with  such  speed 
that  when  the  first  beat  has  reached  X,  A  has  reached 
the  point  B.  Then  the  seven  beats  made  by  A  while 
the  first  beat  is  travelling  from  A  to  X,  and  A  travel- 
ling from  A  to  B,  will  be  crowded  into  the  space  B  X, 
so  that  each  wave  will  be  one-seventh  shorter  than 
before.  In  other  words,  the  wave-lengths  of  the  light 
emitted  by  any  moving  body  will  be  less  or  greater 
according  as  the  motion  is  in  the  direction  in  which 
its  light  is  transmitted,  or  in  the  opposite  direction. 

The  position  of  a  ray  in  the  spectrum  depends 
solely  on  the  wave-length  of  the  light.  It  follows 
that  the  rays  produced  by  any  substance  will  be  dis- 
placed toward  the  blue  or  red  end  of  the  spectrum, 
according  as  the  body  emitting  or  absorbing  the  rays 
is  moving  towards  or  from  us.  This  method  of  deter- 
mining the  motions  of  bodies  to  or  from  us  has  been 
perfected  by  photographing  the  spectrum  of  a  star,  or 
other  heavenly  body,  side  by  side  with  that  of  a  ter- 
restrial substance  rendered  incandescent  in  the  tube 
of  a  telescope.  The  rays  of  this  substance  pass 
through  the  same  spectroscope  as  those  from  the 
star,  so  that,  if  the  wave-lengths  of  the  lines  produced 
by  the  substance  were  the  same  as  those  found  in 
the  star  spectrum,  the  two  lines  would  correspond 
in  position.  The  minute  difference  found  on  the 
photographic  plate  is  the  measure  of  the  velocity 


Si  PROPER  MOTIONS  OF  THE  STARS 

of   the    star    in    the    line   of   sight   called    its    radial 
motion. 


SPECTROGRAM  OF  POLARIS  TAKEN  BY  CAMPBELL  AT  THE  LICK  OBSERVATORY 
The  bright  cross-lines  are  those  of  the  comparison-spectrum  of  iron 

These  measures  require  apparatus  and  manipulation 
of  extraordinary  delicacy,  in  order  to  avoid  every  pos- 
sible source  of  error.  The  displacement  of  the  lines 
produced  by  the  motion  is  in  fact  so  minute  that  great 
skill  is  required  to  make  it  evident,  unless  in  excep- 
tional cases. 

It  will  be  seen  that  the  conclusion  as  to  radial  mo- 
tion depends  on  the  hypothesis  that  the  position  of 
any  ray  produced  by  a  substance  is  affected  by  no 
cause  but  the  motion  of  the  substance.  How  and 


RADIAL  MOTIONS  OF  THE  STARS  85 

when  this  hypothesis  may  fail  is  a  very  important 
question.  It  is  found,  for  example,  that  the  position 
of  a  spectral  ray  may  be  altered  by  compressing  the 
gas  emitting  or  absorbing  the  ray ;  and  it  may  be  in- 
quired whether  the  results  for  motion  in  the  line  of 
sight  may  not  be  vitiated  by  the  absorbing  atmo- 
sphere of  the  star  being  under  heavy  pressure,  thus 
displacing  the  absorption  line. 

To  this  it  may  be  replied  that,  in  any  case,  the 
outer  layers  of  the  atmosphere,  through  which  the 
light  must  last  pass,  are  not  underpressure.  How  far 
the  inner  portions  may  produce  an  absorption  spec- 
trum we  cannot  discuss  at  present,  but  it  does  not 
seem  likely  that  serious  errors  are  thus  introduced  in 
many  cases. 

In  the  measures  made  by  Vogel  at  Potsdam  the 
substance  used  for  comparison  was  generally  hydro- 
gen, the  lines  of  this  substance  being  frequently  very 
sharp  in  the  spectrum  of  the  stars.  The  spectrum  of 
iron  can  also  be  used  for  comparison.  The  stars 
measured  by  Vogel  are  forty-seven  in  number,  all 
brighter  than  the  third  magnitude,  this  being  about 
the  limit  which  his  instrument  could  reach.  Out  of 
his  forty-seven  stars  he  found  four  to  be  affected  with 
a  periodic  inequality  and  therefore  to  belong  to  the 
class  of  binary  systems  to  be  described  in  a  subsequent 
chapter. 

About  1892  Belopolsky  of  Pulkova  continued  Vo- 
gel's  work  with  a  much  larger  instrument,  detecting 
several  other  periodic  motions.  One  of  his  most  in- 
teresting discoveries  was  a  periodic  motion  in  the  star 


86 


PROPER  MOTIONS  OF  THE  STARS 


Eta  Aquilse  corresponding  in  period  to  the  variations 
of  its  light.  He  also  detected  in  Castor  a  variation 
with  a  period  of  about  three  days.  Another  of  his 
discoveries  was  the  very  rapid  motion  of  seventy  kilo- 
metres per  second  in  the  motion  of  Zeta  Herculis. 
This,  however,  is  exceeded  by  the  motion  of  eighty- 
seven  kilometres  which  Campbell  discovered  in  a 
star  of  Cepheus.  Large  though  these  motions  are, 
they  fall  much  below  those  that  belong  to  Arcturus 
and  1830  Groombridge. 


THE  MILLS  SPECTROQRAPH  OF  THE  LICK  OBSERVATORY 

During  the  last  few  years  another  step  forward  has 
been  made  by  Campbell  of  the  Lick  Observatory 
with  the  Mills  spectrograph.1  In  order  to  reach 

"'  It  may  be  remarked  in  this  connection  that  Mr.  D.  O.  Mills,  the  donor  of 
this  instrument,  was  one  of  the  original  trustees  charged  by  Mr.  Lick  in  1874 
tvith  the  construction  of  his  Observatory. 


MOTION  OF  THE  SUN  87 

fainter  stars  than  ever  before,  a  longer  exposure  of  the 
photographic  plate  was  necessary.  A  difficulty  is  met 
with  in  the  prolonged  exposure,  owing  to  the  change 
of  temperature  of  the  apparatus,  which  alters  the  re- 
fracting power  of  the  prisms.  This  difficulty  was 
obviated  by  protecting  the  apparatus  from  such 
changes.  With  this  great  increase  in  photographic 
power  and  time  of  exposure  it  is  now  possible  to 
photograph  the  spectra  of  stars  down  to  the  6th  or 
7th  magnitude.  But  it  is  not  all  stars  that  can  thus 
be  measured,  because,  in  many  cases,  the  spectral  lines 
of  the  star  are  not  sufficiently  sharp  and  well  defined. 

When  a  star  is  found  to  be  seemingly  in  motion, 
as  described  in  the  last  section,  we  may  ascribe  the 
phenomenon  to  a  motion  either  of  the  star  The  Motion 
itself  or  of  the  observer.  In  fact  no  motion  of  the  Sun. 
can  be  determined  or  defined  except  by  reference  to 
some  body  supposed  to  be  at  rest.  In  the  case  of  any 
one  star,  we  may  equally  well  suppose  the  star  to  be 
at  rest  and  the  observer  in  motion,  or  the  contrary. 
Or  we  may  suppose  both  to  have  such  motions  that  the 
difference  of  the  two  shall  represent  the  apparent 
movement  of  the  star.  Hence  our  actual  result  in  the 
case  of  each  separate  star  is  a  relation  between  the 
motion  of  the  star  and  the  motion  of  the  sun. 

I  say  the  motion  of  the  sun  and  not  of  the  earth, 
because,  although  the  observer  is  actually  on  the  earth, 
yet  the  latter  never  leaves  the  neighbourhood  of  the 
sun,  and,  as  a  matter  of  fact,  the  ultimate  result  in  the 
long  run  must  be  a  motion  relative  to  the  sun  itself,  as 
if  we  made  our  observations  from  that  body.  The 


88  PROPER  MOTIONS  OF  THE  STARS 

question  then  arises  whether  there  is  any  criterion  for 
determining  how  much  of  the  apparent  motion  of  any 
given  star  should  be  attributed  to  the  star  itself  and 
how  much  to  a  motion  of  the  sun  in  the  opposite 
direction. 

If  we  should  find  that  the  stars,  in  consequence  of 
their  proper  motions,  all  appeared  to  move  in  the 
same  direction,  we  would  naturally  assume  that  they 
were  at  rest  and  the  sun  in  motion.  A  conclusion  of 
this  sort  was  first  reached  by  Herschel,  who  observed 
that  among  the  stars  having  notable  proper  motions 
there  was  a  general  tendency  to  move  from  the  direc- 
tion of  the  constellation  Hercules,  which  is  in  the 
northern  hemisphere,  towards  the  opposite  constella- 
tion Argo,  in  the  southern  hemisphere. 

Acting  on  this  suggestion,  succeeding  astronomers 
have  adopted  the  practice  of  considering  the  general 
average  of  all  the  stars,  or  a  position  which  we  may 
regard  as  their  common  centre  of  gravity,  to  be  at 
rest,  and  then  determining  the  motion  of  the  sun  with 
respect  to  this  centre.  Here  we  encounter  the  diffi- 
culty that  we  cannot  make  any  absolute  determina- 
tion of  the  position  of  such  a  centre.  The  latter 
will  vary  according  to  what  particular  stars  we  are 
able  to  include  in  our  estimate.  What  we  can  do  is 
to  take  all  the  stars  which  appear  to  have  a  proper 
motion,  and  determine  the  general  direction  of  that 
motion.  This  gives  us  a  certain  point  in  the  heavens 
toward  which  the  solar  system  is  travelling,  and  which 
is  now  called  the  solar  apex,  or  "  the  apex  of  the  solar 
way." 


MOTION  OF  THE  SUN  89 

The  apparent  motion  of  the  stars  away  from  the 
apex,  and  due  to  this  motion  of  the  solar  system,  is 
now  called  their  parallactic  motion,  to  distinguish  it 
from  the  actual  motion  of  the  star  itself. 

The  interest  which  attaches  to  the  position  of  the 
solar  apex  has  led  a  great  number  of  investigators  to 
determine  it.  Owing  to  the  rather  indefinite  charac- 
ter of  the  material  of  investigation,  the  uncertainty  of 
the  proper  motions,  and  the  additions  constantly  made 
to  the  number  of  stars  which  are  available  for  the 
purpose  in  view,  different  investigators  have  reached 
different  results.  Until  quite  recently,  the  general 
conclusion  was  that  the  solar  apex  was  situated  some- 
where in  the  constellation  Hercules.  But  the  general 
trend  of  recent  research  has  been  to  place  it  in  or  near 
the  adjoining  constellation  Lyra.  This  change  has 
arisen  mainly  from  including  a  larger  number  of  stars, 
whose  motions  were  determined  with  greater  accuracy. 

Former  investigators  based  their  conclusions  en- 
tirely on  stars  having  considerable  proper  motions, 
these  being,  in  general,  the  nearer  to  us.  The  fact 
is,  however,  that  it  is  better  to  include  stars  having  a 
small  proper  motion,  because  the  advantage  of  their 
great  number  more  than  counterbalances  the  disad- 
vantage of  their  distance. 

The  conclusions  reached  by  some  recent  investigat- 
ors of  the  position  of  the  solar  apex  are  as  follows  : 
We  call  A  the  right  ascension  of  the  apex ;  D  its 
declination. 

Prof.  Lewis  Boss,  from  273  stars  of  large  proper 
motion,  found : 


90  PROPER  MOTIONS  OF  THE  STARS 

A=283°.3;  D  =  44°.i. 

If  he  excluded  the  motions  of  26  stars  which  exceeded 
40"  per  century  the  result  was 

A  =  288°.7;  D  =  5i°.s. 

A  comparison  or  these  numbers  shows  how  much  the 
result  depends  on  the  special  stars  selected.  By 
leaving  out  26  stars  the  apex  is  changed  by  5°  in  R. 
A.  and  7°  in  declination. 

It  is  to  be  remarked  that  the  stars  used  by  Boss 
are  all  contained  in  a  belt  four  degrees  wide,  extend- 
ing from  i°  to  5°  north  of  the  equator. 

Dr.  Oscar  Stumpe,  of  Berlin,  made  a  list  of  996 
stars  having  proper  motions  between  16"  and  128" 
per  century.  He  divided  them  into  three  groups, 
the  first  including  those  between  16"  and  32"  ;  the 
second  between  32"  and  64" ;  the  third  between  64" 
and  128".  The  number  of  stars  in  each  group  and 
the  position  of  the  apex  derived  from  them  are  as 
follows : 

Gr.  I,  551  stars  ;  A  =  287°.4  ;  D  =  +45°.o 

H,  339  282°.2  43°.5 

III,  106  28o°.2  33°-5 

Porter,  of  Cincinnati,  made  a  determination  from  a 
yet  larger  list  of  stars  with  results  of  the  same  gen- 
eral character. 

These  determinations  have  the  advantage  that  the 
stars  are  scattered  over  the  entire  heavens,  the  south- 
ern as  well  as  the  northern  ones.  The  difference  of 
more  than  10°  between  the  position  derived  from 
stars  with  the  largest  proper  motions,  and  from  the 
other  stars,  is  remarkable. 


MOTION  OF  THE  SUN  91 

The  present  writer,  in  a  determination  of  the  pre- 
cessional  motion,  incidentally  determined  the  solar 
motion  from  2527  stars  contained  in  Bradley's  Cata- 
logue which  had  small  proper  motions,  and  from 
about  600  more  having  larger  proper  motions.  Of 
the  latter  the  declinations  only  were  used.  The  re- 
sults were : 

From  small  motions  :  A  =  274°. 2  ;  D  =  +3i°.2 
From  large  motions  :  276°. 9  3i°-4 

Quite  recently  Campbell  has  made  a  determination 
of  the  position  of  apex  from  the  radial  motions  of  280 
stars,  mostly  measured  by  himself.  The  result  is : 

A=    277°.5 
D  =  -f-2o°-° 

From  all  these  results  it  would  seem  that  the  most 
likely  apex  of  the  solar  motion  is  toward  a  point  in 

Right  Ascension,  280° 
Declination,  35°  north 

This  point  is  situated  in  the  constellation  Lyra, 
about  4°  from  the  first-magnitude  star  Vega.  The 
uncertainty  of  the  result  is  as  much  as  this  difference, 
4°  or  5°  at  least.  We  may  therefore  state  the  con- 
clusion in  this  form  : 

The  apex  of  the  solar  motion  is  in  the  general  direc- 
tion of  the  constellation  Lyra,  and  perhaps  near  the 
star  Vega,  the  brightest  of  that  constellation. 

It  must  be  admitted  that  the  wide  difference  be- 
tween the  positions  of  the  apex  from  large  and  from 
small  proper  motions,  as  found  by  Porter,  Boss,  and 
Stumpe,  requires  explanation.  Since  the  apparent 


92  PROPER  MOTIONS  OF  THE  STARS 

motions  of  the  stars  are  less  the  greater  their  dis- 
tance, these  results,  if  accepted  as  real,  would  lead  to 
the  conclusion  that  the  position  of  the  solar  apex 
derived  from  stars  near  to  us  was  much  farther  south 
than  when  derived  from  more  distant  stars.  This, 
again,  would  indicate  that  our  sun  is  one  of  a  cluster 
or  group  of  stars  having,  in  the  general  average,  a 
different  proper  motion  from  the  more  distant  stars. 
But  this  conclusion  is  not  to  be  accepted  as  real  until 
the  subject  has  been  more  fully  investigated.  The 
result  may  depend  on  the  selection  of  the  stars  ;  and 
there  is,  as  yet,  no  general  agreement  among  investigat- 
ors as  to  the  best  way  of  making  the  determination. 

The. next  question  which  arises  is  that  of  the  ve- 
locity of  the  solar  motion.  The  data  for  this  de- 
termination are  more  meagre  and  doubtful  than  those 
for  the  direction  of  the  motion.  The  most  obvious 
and  direct  method  is  to  determine  the  parallactic 
motion  of  the  stars  of  known  parallax.  Regarding 
any  star  90°  from  the  apex  of  the  solar  motion  as  in 
a  state  of  absolute  rest,  we  have  the  obvious  rule  that 
the  quotient  of  its  parallactic  motion  during  any 
period,  say  a  century,  divided  by  its  parallax,  gives 
the  solar  motion  during  that  period,  in  units  of  the 
earth's  distance  from  the  sun.  In  fact,  by  a  motion 
of  the  sun  through  one  such  unit,  the  star  would  have 
an  apparent  motion  in  the  opposite  direction  equal  to 
its  annual  parallax.  If  the  star  is  not  90°  from  the 
apex  we  can  easily  reduce  its  observed  parallactic 
motion  by  dividing  it  by  the  sine  of  its  actual  dis- 
tance from  the  apex. 


MOTION  OF  THE  SUN  93 

Since  every  star  has,  presumably,  a  proper  motion 
of  its  own,  we  can  draw  no  conclusion  from  the 
apparent  motion  of  any  one  star,  owing  to  the  impos- 
sibility of  distinguishing  its  actual  from  its  parallactic 
motion.  We  should,  therefore,  base  our  conclusion 
on  the  mean  result  from  a  great  number  of  stars, 
whose  average  position  or  centre  of  mass  we  might 
assume  to  be  at  rest.  Here  we  meet  the  difficulty 
that  the  stars  measured  for  parallax  are  generally 
those  having  a  proper  motion  away  from  the  apex. 
This  will  make  the  result  derived  in  this  way  too 
large. 

A  second  method  is  based  on  measures  of  the 
motion  of  stars  in  the  line  of  sight.  A  star  at  rest 
in  the  direction  of  the  solar  apex  would  be  apparently 
moving  towards  us  with  a  velocity  equal  to  that  of 
the  solar  motion.  Assuming  the  centre  of  mass  of 
all  the  stars  observed  to  be  at  rest,  we  should  get  the 
solar  motion  from  the  mean  of  all.  In  the  investiga- 
tion just  referred  to,  Campbell  has  derived  the  ve- 
locity, 19.89  kilometres  per  second,  with  a  probable 
error  of  1.52  kilometres.  A  speed  of  19  kilometres 
per  second  would  carry  our  system  over  almost  ex- 
actly four  radii  of  the  earth's  orbit  in  a  year,  and 
we  may  regard  this  as  the  most  likely  value  of  the 
speed  in  question. 


CHAPTER    VII 

VARIABLE  STARS 

— And  the  moist  star     .     .     . 
Was  sick  almost  to  doomsday  with  eclipse. — SHAKESPEARE. 

IT  is  a  curious  fact  that  the  ancient  astronomers, 
notwithstanding  the  care  with  which  they  ob- 
served the  heavens,  never  noticed  that  any  of  the 
stars  changed  in  brightness.  The  earliest  record  of 
such  an  observation  dates  from  1596,  when  the  peri- 
odical disappearance  of  Omicron  Ceti  was  noticed. 
After  this,  nearly  two  centuries  elapsed  before  another 
case  of  variability  in  a  star  was  recorded.  During 
the  first  half  of  the  nineteenth  century  Argelander  so 
systematised  the  study  of  variable  stars  as  to  make  it 
a  new  branch  of  astronomy.  In  recent  years  it  has 
become  of  capital  interest  and  importance  through 
the  development  of  spectroscopic  research. 

Students  who  are  interested  in  the  subject  will  find 
the  most  complete  information  attainable  in  the  cata- 
logues of  variable  stars  published  from  time  to  time 
by  Chandler  in  the  Astronomical  Journal.  His  third 
catalogue,  which  appeared  in  1896,  comprises  more 
than  three  hundred  stars  whose  variability  has  been 

94 


CLASSES  OF  VARIABLE  STARS  95 

well  established,  while  there  is  always  a  long  list  of 
"  suspected  variables  " — whose  cases  are  still  to  be 
tried.  The  number  to  be  included  in  the  established 
list  is  continually  increasing  at  such  a  rate  that  it  is 
impossible  to  state  it  with  any  approximation  to  ex- 
actness. The  possibility  of  such  a  statement  has 
been  yet  further  curtailed  by  the  recent  discovery  at 
the  Harvard  Observatory  that  certain  clusters  of  stars 
contain  an  extraordinary  proportion  of  variables. 
Altogether  at  the  time  of  the  latest  publication,  509 
such  stars  were  found  in  twenty-three  clusters.  The 
total  number  of  these  objects  in  clusters,  therefore, 
exceeds  the  number  known  in  the  rest  of  the  sky. 
They  will  be  described  more  fully  in  a  subsequent 
chapter.  For  the  present  we  are  obliged  to  leave 
this  rich  field  out  of  consideration  and  confine  our 
study  to  the  isolated  variable  stars  which  are  found 
in  every  region  of  the  heavens. 

Variable  stars  are  of  several  classes,  which,  how- 
ever, run  into  each  other  by  gradations  so  slight  that 
a  sharp  separation  cannot  always  be  made  between 
them.  Yet  there  are  distinguishing  features,  each  of 
which  marks  so  considerable  a  number  of  these  stars 
as  to  show  some  radical  difference  in  the  causes 
on  which  the  variations  depend. 

We  have  first  to  distinguish  the  two  great  classes 
of  irregular  and  periodic  stars.  The  irregular  ones 
increase  and  diminish  in  so  fitful  a  way  that  no  law  of 
their  change  can  be  laid  down.  To  this  class  belong 
the  so-called  "  new  stars,"  which  at  various  periods  in 
history  have  blazed  out  in  the  heavens,  and  then  in 


96  VARIABLE  STARS 

a  few  weeks  or  months  have  again  faded  away.  It  is 
a  remarkable  fact  that  no  star  of  the  latter  class  has 
ever  been  known  to  blaze  out  more  than  once. 
This  fact  distinguishes  new  stars  from  other  irregu- 
larly variable  ones. 

Periodic  stars  are  those  which  go  through  a  regular 
cycle  of  changes  in  a  definite  interval  of  time,  so  that, 
Periods  after  a  certain  number  of  days,  sometimes 
of  Variable  of  hours,  the  star  returns  to  the  same  bright- 
ness. But  even  in  the  case  of  periodic 
stars,  it  is  found  that  the  period  is  more  or  less  vari- 
able, and  in  special  cases  the  amount  of  the  variation 
is  such  that  it  cannot  always  be  said  whether  we 
should  call  a  star  periodic  or  irregular. 

The  periodic  stars  show  wide  differences,  both  in 
the  length  of  the  period  and  in  the  character  of  the 
changes  they  undergo.  In  most  cases  they  increase 
rapidly  in  brightness  during  a  few  days  or  weeks,  and 
then  slowly  fade  away,  to  go  through  the  same 
changes  again  at  the  end  of  the  period.  Some  stars 
are  distinguished  more  especially  by  their  maxima, 
or  periods  of  greatest  brightness,  while  others  are 
more  sharply  marked  by  minima,  or  periods  of  least 
brightness.  In  some  cases  there  are  two  unequal 
maxima  or  minima  in  the  course  of  a  period. 

Chandler's  third  catalogue  of  variable  stars  gives 
the  periods  of  280  of  these  objects,  which  seem  to 
have  been  fairly  well  made  out.  Mr.  A.  W.  Roberts 
has  added  an  important  number  of  southern  stars  in 
a  list  found  in  the  Astronomical  Journal,  xxi.,  p.  84.  A 
classification  of  these  periods,  as  to  their  length,  will 


PERIODS  OF  VARIABLE  STARS 


97 


be  interesting.  The  first  set  of  numbers  in  the  fol- 
lowing table,  headed  C.,  are  the  periods  of  Chandler's 
catalogue,  the  next,  headed  R.,  are  the  additional 
periods  given  by  Roberts.  There  are  of  periods 


Leg 

BetN 

than  50  c 
veen  50  a 

100 

150 
200 
250 
300 
350 
400 
450 
500 
550 
600 

C. 
lays        -  -         •       -  fv* 

R. 
10 

2 

3 
4 

12 

5 
5 
6 

2 

o 
o 
I 
o 

Sum 
73Sta 

8 

12 

22 
41 

45 
49 
50 

20 

6 

I 

2 
I 

nd  too  da 
150 
200 
250 
300 
350 
400 
450 
500 
550 
600 
6<;o 

g 

18 

....      29 

18 

6 

I 

....     .      I 

.1 

It  will  be  seen  from  this  that,  leaving  out  the  cases 
of  very  short  period,  the  greater  number  of  the 
periods  fall  between  300  and  400  days.  From  this 
value  the  number  falls  off  in  both  directions.  Only 
four  periods  exceed  500  days,  and  of  these  the  long- 
est is  610  days.  We  infer  from  this  that  there  is 
something  in  the  constitution  of  these  stars,  or  in  the 
causes  on  which  their  variation  depends,  which  limits 
the  period.  This  limitation  establishes  a  well-marked 
distinction  between  the  periodic  stars  and  the  irreg- 
ular variables  to  be  hereafter  described. 

Returning  to  the  upper  end  of  the  scale,  the  con- 
trast between  the  great  number  of  stars  less  than 
50  days,  and  the  small  number  between  50  and  100 
seems  to  show  that  we  have  here  a  sharp  line  of 
distinction  between  stars  of  long  and  those  of  short 
period.  But  when  we  examine  the  matter  in  detail 
we  find  that  the  statistics  of  the  periods  do  not 


98 


VARIABLE  STARS 


enable  us  to  draw  any  such  line.  Among  isolated 
stars  about  ten  periods  are  less  than  one  day,  and  the 
number  of  this  class  known  to  us  is  continually  in- 
creasing. Forty  or  fifty  are  between  one  and  ten 
days,  and  from  this  point  upwards  they  are  scattered 
with  a  fair  approach  to  equality  up  to  a  period  of  100 
days.  There  is,  however,  a  possible  distinction, 
which  we  shall  develop  presently. 

The  law  of  change  in  a  variable  star  is  represented 
to  the  eye  by  a  curve  in  the  following  way  :     We 
draw  a  straight  horizontal  line  A  X  to  re- 
present the  time.     A  series  of  equidistant 

pO}ntSj  ^  ^  ^  ^    etc  ?    on    ^[s    ]jne    WJU    re_ 

present  moments  of  time.  One  of  the  spaces,  a,  b, 
etc.,  may  represent  an  hour,  a  day,  or  a  month,  accord- 


Light- 
curve 
of  a  Star. 


.< 

A 

M 

0 
t 

"V 

fr 

TTTTTfl 

-"' 

X 


ing  to  the  rapidity  of  change.  We  take  a  to  represent 
the  initial  moment,  and  erect  an  ordinate,  a  a,  of  such 
length  as  to  represent  the  brightness  of  the  star  on 
some  convenient  scale  at  this  moment.  At  the  second 
moment,  b,  which  may  be  an  hour  or  a  day  later,  we 
erect  another  ordinate,  b  b ',  representing  the  brightness 
at  this  moment.  We  continue  this  process  as  long 
as  may  be  required.  Then  we  draw  a  curve,  repre- 
sented by  the  dotted  line,  through  the  ends  of  all  the 


TYPES  OF  VARIABLE  STARS  99 

ordinates.  In  the  case  of  a  periodic  star  it  is  only 
necessary  to  draw  the  curve  through  a  single  period, 
since  its  continuation  will  be  a  repetition  of  its  form 
for  any  one  period. 

We  readily  see  that  if  a  star  does  not  vary,  all  the 
ordinates  will  be  of  equal  length,  and  the  curve  will 
be  a  horizontal  straight  line.  Moreover,  the  curve 
will  take  this  form  through  any  portion  of  time  dur- 
ing which  the  light  of  the  star  is  constant. 

There  are  three  of  the  periodic  stars  plainly  visible 
to  the  naked  eye  at  maximum,  of  which  Types  of 
the  variations  are  so  wide  that  they  may  Variable 
easily  be  noticed  by  anyone  who  looks  for 
them  at  the  right  times,  and  knows  how  to  find  the 
stars.  These  stars  are  : 

Omicron  Ceti,  called  also  Mira  Ceti. 

Beta  Persei,  or  Algol. 

Beta  Lyrae. 

It  happens  that  each  of  these  stars  exemplifies  a 
certain  type  or  law  of  variation. 

On  August  13,  1596,  David  Fabricius  noticed  a 
star  in  the  constellation  Cetus  which  was  not  found 
in  any  catalogue.  Bayer,  in  his  Uranomet-  The  Ceti 
ria,  of  which  the  first  edition  was  published  Type- 
in  1 60 1,  marked  the  star  Omicron,  but  said  nothing 
about  the  fact  that  it  was  visible  only  at  certain  times. 
Fabricius  observed  the  star  from  time  to  time  until 
1609,  but  he  does  not  appear  to  have  fully  and  accur- 
ately recognised  its  periodicity.  But  so  extraordin- 
ary an  object  could  not  fail  to  command  the  attention 
of  astronomers,  and  the  fact  was  soon  established  that 


TOO  VARIABLE  STARS 

the  star  appeared  at  intervals  of  about  eleven  months, 
gradually  fading  out  of  sight  after  a  few  weeks  of 
visibility.  Observations  of  more  or  less  accuracy 
having  been  made  for  more  than  two  centuries,  the 
following  facts  respecting  it  have  been  brought  to 
light : 

Its  variations  are  somewhat  irregular.  Sometimes, 
when  at  its  brightest,  it  rises  nearly  or  quite  to  the 
second  magnitude.  This  was  the  case  in  October, 
1898,  when  it  was  about  as  bright  as  Alpha  Ceti.  At 
other  times  its  maximum  brightness  scarcely  exceeds 
the  fifth  magnitude.  No  law  has  yet  been  discovered 
by  which  it  can  be  predicted  whether  it  will  attain 
one  degree  of  brightness  or  another  at  maximum. 

Its  minima  are  also  different.  Sometimes  it  sinks 
only  to  the  eighth  magnitude ;  at  other  times  to  the 
ninth  or  lower.  In  either  case  it  is  invisible  to  the 
naked  eye. 

As  with  other  stars  of  this  kind,  it  brightens  up 
more  rapidly  than  it  fades  away.  It  takes  a  few 
weeks  from  the  time  it  becomes  visible  to  reach  its 
greatest  brightness,  whatever  that  may  be.  It  gener- 
ally retains  this  brightness  for  two  or  three  weeks, 
then  fades  away,  gradually  at  first,  afterwards  more 
rapidly.  The  whole  time  of  visibility  will,  therefore, 
be  two  or  three  months.  Of  course,  it  can  be  seen 
with  a  telescope  at  any  time. 

The  period  also  is  different  in  a  somewhat  irregular 
way.  If  we  calculate  when  the  star  ought  to  be  at  its 
greatest  brightness  on  the  supposition  that  the  inter- 
vals between  the  maxima  ought  to  be  equal,  we  shall 


Mjr±rj\s\  i  mni i 1 1    \jr  AOt.  nun  \rm.  M. 

UNIVERSITY  OF  CALIFORNIA 
AT  LOS  ANGELES 

THE  ALGOL   TYPE  101 

find  that  sometimes  the  maximum  will  be  thirty  or 
forty  days  early  and  at  other  times  thirty  or  forty 
days  late.  These  early  or  late  maxima  follow  each 
other  year  after  year,  with  a  certain  amount  of 
regularity  as  regards  the  progression,  though  no  de- 
finable law  can  be  laid  down  to  govern  them.  Thus, 
during  the  period  from  1782  to  1800  it  was  from 
thirteen  to  twenty-four  days  late.  In  1812  it  was 
thirty-nine  days  late.  From  1845  to  1856  it  was  on 
the  average  about  a  month  too  early.  Several  recent 
maxima,  notably  those  from  1895  to  1898,  again  oc- 
curred late.  Formulae  have  been  constructed  to  show 
these  changes,  but  there  is  no  certainty  that  they  ex- 
press the  actual  law  of  the  case.  Indeed,  the  proba- 
bility seems  to  be  that  there  is  no  invariable  law  that 
we  can  discover  to  govern  it. 

Argelander  fixed  the  length  of  the  period  at  331.9 
days.  More  recently,  Chandler  fixed  it  at  331.6  days. 
It  would  seem,  therefore,  to  have  been  somewhat 
shorter  in  recent  times.  It  was  at  its  maximum  to- 
ward the  end  of  October,  1898.  We  may  therefore 
expect  that  future  maxima  will  occur  in  June,  1902  ; 
May,  1903;  April,  1904;  March,  1905,  and  so  on, 
about  a  month  earlier  each  year.  During  the  few 
years  following  1903  the  maxima  will  probably  not  be 
visible,  owing  to  the  star  being  near  conjunction  with 
the  sun  at  the  times  of  their  occurrence. 

The  star  Algol,  or  Beta  Persei,  as  it  is  commonly 
called  in  astronomical  language,  may,  in  The  Algol 
northern  latitudes,  be  seen  on  almost  any  Type, 
night  of  the  year.  In  the  early  summer  we  should 


102  VARIABLE  STARS 

probably  see  it  only  after  midnight,  in  the  north-east. 
In  late  winter  it  would  be  seen  in  the  north-west. 
From  August  until  January  one  can  find  it  at  some 
time  in  the  evening  by  becoming  acquainted  with  the 
constellations.  It  is  nearly  of  the  second  magnitude. 
One  might  look  at  it  a  score  of  times  without  seeing 
that  it  varied  in  brilliancy.  But  at  certain  stated  in- 
tervals, somewhat  less  than  three  days,  it  fades  away 
to  nearly  the  fourth  magnitude  for  a  few  hours,  and 
then  slowly  recovers  its  light.  This  fact  was  first  dis- 
covered by  Goodrick  in  1783,  since  which  time  the 
variations  have  been  carefully  followed.  The  law  of 
variation  thus  defined  is  expressed  by  a  curve  of  the 
following  form : 


The  idea  that  what  we  see  in  the  star  is  a  partial 
eclipse  caused  by  a  dark  body  revolving  round  it,  was 
naturally  suggested  even  to  the  earliest  observers.  But 
it  was  impossible  to  test  this  theory  until  recent  times. 
Careful  observation  showed  changes  in  the  period  be- 
tween the  eclipses,  which,  although  not  conclusive 
against  the  theory,  might  have  seemed  to  make  it 
somewhat  unlikely.  The  application  of  the  spectro- 
scope to  the  determination  of  radial  motions  enabled 
Vogel,  of  Potsdam,  in  1889,  to  set  the  question  at 
rest.  His  method  of  reasoning  and  proceeding  was 
this: 

If  the  fading  out  which  we  see  is  really  due  to  an 
eclipse  by  a  dark  body,  that  body  must  be  nearly  or 


THE  ALGOL  TYPE  103 

quite  as  large  as  the  star  itself,  else  it  could  not  cut 
off  so  much  of  its  light.  In  this  case,  it  is  probably 
nearly  as  massive  as  the  star  itself,  and  therefore 
would  affect  the  motion  of  the  star.  Both  bodies 
would,  in  fact,  revolve  around  their  common  centre 
of  gravity.  Therefore  when,  after  the  dark  body  has 
passed  in  front  of  the  star,  it  has  made  one-fourth  of 
a  revolution,  which  would  require  about  seventeen 
hours,  the  star  would  be  moving  towards  us.  Again, 
seventeen  hours  before  the  eclipse,  it  ought  to  be 
moving  away  from  us. 

The  measurement  of  six  photographs  of  the  spec- 
trum, of  which  four  were  taken  before  the  eclipses 
and  two  afterward,  gives  the  following  results  : 

Before  eclipses  :  Velocity  from  the  sun  equals  39  km.  per 
second. 

After  eclipses  :  Velocity  toward  the  sun  equals  47  km.  per 
second. 

These  results  show  that  the  hypothesis  in  question 
is  a  true  one,  and  afforded  the  first  conclusive  evid- 
ence of  a  dark  body  revolving  around  a  distant  star. 
A  study  of  the  law  of  diminution  and  recovery  of  the 
light  during  the  eclipse,  combined  with  the  preceding 
motions,  enabled  Vogel  to  make  an  approximate  es- 
timate of  the  size  of  the  orbit  and  of  the  two  bodies. 
The  star  itself  is  somewhat  more  than  a  million  of 
miles  in  diameter ;  the  dark  companion  a  little  less. 
The  latter  is  about  the  size  of  our  sun.  Their  dis- 
tance apart  is  somewhat  more  than  three  millions 
of  miles ;  the  respective  masses  are  about  one-half 


104  VARIABLE  STARS 

and  one-fourth  that  of  the  sun.  These  results,  though 
numerically  rather  uncertain,  are  probably  near 
enough  to  the  truth  to  show  us  what  an  interesting 
system  we  here  have  to  deal  with.  We  can  say  with 
entire  certainty  that  the  size  and  mass  of  the  dark 
body  exceed  those  of  any  planet  of  our  system,  even 
Jupiter,  several  hundredfold. 

The  period  of  the  star  is  also  subject  to  variations 
of  a  somewhat  singular  character.  These  have  been 
attributed  by  Chandler  to.  a  motion  of  the  whole  sys- 
tem around  a  third  body,  itself  invisible.  This  theory 
is,  however,  still  to  be  proved.  Quite  likely  the  planet 
which  causes  the  eclipse  is  not  the  only  one  which 
revolves  around  this  star.  The  latter  may  be  the 
centre  of  a  system  like  our  solar  system,  and  the  other 
planets  may,  by  their  action,  cause  changes  in  the 
motion  of  the  body  that  produces  the  eclipses.  The 
most  singular  feature  of  the  change  is  that  it  seems 
to  have  taken  place  quite  rapidly  about  1840.  The 
motion  was  nearly  uniform  up  to  near  this  date  ;  then 
it  changed,  and  again  remained  nearly  uniform  until 
1890.  Since  then  not  enough  of  observations  have 
been  published  to  test  the  laws  of  change  conclus- 
ively. 

It  is  found  that  several  other  stars  vary  in  the  same 
way  as  Algol ;  that  is  to  say,  they  are  invariable  in 
brightness  during  the  greater  part  of  the  time,  but 
fade  away  for  a  few  hours  at  regular  intervals.  This 
is  a  kind  of  variation  which  it  is  most  difficult  to  dis- 
cover, because  it  will  be  overlooked  unless  the  ob- 
server happens  to  notice  the  star  during  the  time 


THE  ALGOL  TYPE  105 

when  an  eclipse  is  in  progress,  and  is  thoroughly 
aware  of  its  previous  brightness.  One  might  observe 
a  star  of  this  kind  very  accurately  a  score  of  times, 
without  hitting  upon  the  right  moment.  On  the 
principle  that  like  effects  are  due  to  like  causes,  we 
are  justified  in  concluding  that  in  the  cases  of  all 
stars  of  this  type,  the  eclipses  are  caused  by  the  revol- 
ution of  a  dark  body  round  the  principal  star. 

A  feature  of  all  the  Algol  variables  is  the  shortness 
of  the  periods.  The  longest  period  is  less  than  five 
days,  while  three  are  less  than  one  day.  This  is  a 
result  that  we  might  expect  from  the  nature  of  the 
case.  The  nearer  a  dark  planet  is  to  the  star,  the 
more  likely  it  will  be  to  hide  its  light  from  an  ob- 
server at  a  great  distance.  If,  for  example,  the 
planet  Jupiter  were  nearly  as  large  as  the  sun,  the 
chances  would  be  hundreds  to  one  against  the  plane 
of  the  orbit  being  so  nearly  in  the  line  of  a  distant 
observer  that  the  latter  would  ever  see  an  eclipse  of 
the  sun  by  the  planet.  But  if  the  planet  were  close 
to  the  sun,  the  chances  might  increase  to  one  in  ten, 
and  yet  further  to  almost  any  extent,  according  to  the 
nearness  of  the  two  bodies. 

Still,  we  cannot  set  any  definite  limit  to  the  period 
of  stars  of  this  type  ;  all  we  can  say  is  that,  as  the 
period  we  seek  for  increases,  the  number  of  stars 
varying  in  that  period  must  diminish.  This  follows 
not  only  from  the  reason  just  given,  but  from  the 
fact  that  the  longer  the  interval  that  separates  the 
partial  eclipses  of  a  star  of  the  Algol  type,  the  less 
likely  they  are  to  be  detected. 


io6  VARIABLE  STARS 

The  star  Beta  Lyrae  shows  variations  quite  differ- 
ent in  their  nature  from  those  of  Algol,  yet  having  a 
The  certain  analogy  to  them.  Anyone  who  looks 

Beta  Lyrae  at  the  constellation  Lyra  a  few  nights  in 
Type>  succession,  and  compares  Beta  with  Gamma, 
a  star  of  nearly  the  same  brightness  in  its  neighbour- 
hood, will  see  that  while  on  some  evenings  the  stars 
are  of  equal  brightness,  on  others  Beta  will  be  fainter 
by  perhaps  an  entire  magnitude. 

A  careful  examination  of  these  variations  shows  us 
a  very  remarkable  feature.  On  a  preliminary  study, 
the  period  will  seem  to  be  six  and  one-half  days. 
But,  comparing  the  alternate  minima,  we  shall  find 
them  unequal.  Hence  the  actual  period  is  thirteen 
days.  In  this  period  there  are  two  unequal  minima, 
separated  by  equal  maxima.  That  is  to  say,  the 
partial  eclipses  at  intervals  of  six  and  one-half  days 
are  not  equal.  At  the  alternate  minima  the  star 
is  half  as  bright  again  as  at  the  intermediate  minima. 

It  is  impossible  to  explain  such  a  change  as  this 
merely  by  the  interposition  of  a  dark  body,  and  this 
for  two  reasons.  Instead  of  remaining  invariable 
between  the  minima,  the  variation  is  continuous  dur- 
ing the  whole  period,  like  the  rising  and  falling  of 
a  tide.  Moreover,  the  inequality  of  the  alternating 
minima  is  against  the  theory. 

Pickering,  however,  found  from  the  doubling  of 
the  spectral  lines  that  there  were  two  stars  revolving 
round  each  other.  Then  Prof.  G.  W.  Myers,  of 
Indiana,  worked  out  a  very  elaborate  mathematical 
theory  to  explain  the  variations,  which  is  not  less 


THE  BETA  LYR^  TYPE  107 

remarkable  for  its  ingenuity  than  for  the  curious  na- 
ture of  the  system  it  brings  to  light.  His  conclusions 
are  these  : 

Beta  Lyrse  consists  of  two  bodies,  gaseous  in  their 
nature,  which  revolve  round  each  other,  so  near  to- 
gether as  to  be  almost  in  contact.  They  are  of 
unequal  size.  Both  are  self-luminous.  By  their 
mutual  attraction  they  are  drawn  out  into  ellipsoids. 
The  smaller  body  is  much  brighter  than  the  other. 
When  we  see  the  two  bodies  laterally,  they  are  at 
their  brightest.  As  they  revolve,  however,  we  see 
them  more  and  more  end  on,  and  thus  the  light 
diminishes.  At  a  certain  point  one  begins  to  cover 
the  other  and  hide  its  light.  Thus  the  combined 
light  continues  to  diminish  until  the  two  bodies  move 
across  our  line  of  sight.  Then  we  have  a  minimum. 
At  one  minimum,  however,  the  smaller  and  brighter 
of  the  two  bodies  is  projected  upon  the  larger  one, 
and  thus  increases  its  apparent  brilliancy.  At  the 
other  minimum,  it  is  hiding  behind  the  other,  and 
therefore  we  see  the  light  of  the  larger  one  alone. 

This  theory  receives  additional  confirmation  from 
the  fact,  shown  by  the  spectroscope,  that  these  stars 
are  either  wholly  gaseous,  or  at  least  have  self-lumin- 
ous atmospheres.  Some  of  Professor  Myers's  conclu- 
sions respecting  the  magnitudes  are  summarised  as 
follows : 

The  larger  body  is  about  0.4  as  bright  as  the 
smaller. 

The  flattening  of  the  ellipsoidal  masses  is  about 
0.17. 


io8  VARIABLE  STARS 

The  distance  of  centres  is  about  i-J  the  semi-major 
axis  of  the  larger  star,  or  about  50,000,000  kilometres 
(say  30,000,000  miles). 

The  mass  of  the  larger  body  is  about  twice  that  of 
the  smaller,  and  9^  times  the  mass  of  the  sun. 

The  mean  density  of  the  system  is  a  little  less  than 
that  of  air.1 

It  should  be  remarked  that  these  numbers  rest  on 
spectroscopic  results  which  need  further  confirmation. 
They  are  therefore  liable  to  be  changed  by  subse- 
quent investigation.  What  is  most  remarkable  is 
that  we  have  here  to  deal  with  a  case  to  which  we 
have  no  analogy  in  our  solar  system,  and  which  we 
should  never  have  suspected,  had  it  not  been  for 
observations  of  this  star. 

The  gap  between  the  variable  stars  of  the  Algol 
type  and  those  of  the  Beta  Lyrse  type  is  at  the  pre- 
sent time  being  rilled  by  new  discoveries  in  such  a 
way  as  to  make  a  sharp  distinction  of  the  two  classes 
difficult.  It  is  characteristic  of  the  Algol  type  proper 
that  the  partial  eclipses  are  due  to  the  interposition 
of  a  dark  planet  revolving  round  the  bright  star.  But 
suppose  that  we  have  two  nearly  equal  stars,  A  and 
B,  both  bright,  revolving  round  their  common  centre 
of  gravity  in  a  plane  passing  near  our  system.  Then 
A  will  eclipse  B,  and,  half  a  revolution  later,  B  will 
eclipse  A,  and  so  on  in  alternation.  But  when  the 
stars  are  equal  we  may  have  no  way  of  deciding 
which  is  being  eclipsed,  and  thus  we  shall  have  a  star 
of  the  Algol  type  so  far  as  the  law  of  variation  is 

1  Astrophysieal  Journal,  vol.  vii.,  January,  1898. 


THE  BETA  LYR^  TYPE  109 

concerned,  yet,  as  a  matter  of  fact,  belonging  rather 
to  the  Beta  Lyrae  type.  If  the  velocity  in  the  line  of 
sight  could  be  measured,  the  question  would  be  set- 
tled at  once.  But  only  the  brightest  stars  can,  so  far, 
be  thus  measured,  so  that  the  spectroscope  cannot 
help  us  in  the  majority  of  cases. 

The  most  interesting  case  of  this  kind  yet  brought 
to  light  is  that  of  Y  Cygni.  The  variability  of 
this  star,  ordinarily  of  the  fourth  magnitude,  was  dis- 
covered by  Chandler  in  December,  1886.  The  min- 
ima occurred  at  intervals  of  three  days.  But  in  the 
following  summer  he  found  an  apparent  period  of 
i  d.  12  h.,  the  alternate  minima  being  invisible  be- 
cause they  occurred  during  daylight,  or  when  the 
star  was  below  the  horizon.  With  this  period  the 
times  of  minima  during  the  summer  of  1888  were 
predicted. 

It  was  then  found  that  the  times  of  the  alternate 
minima,  which,  as  we  have  just  said,  were  the  only 
ones  visible  during  any  one  season,  did  not  corre- 
spond to  the  prediction.  The  period  seemed  to  have 
greatly  changed.  Afterward,  it  seemed  to  return  to 
its  old  value.  After  puzzling  changes  of  this  sort,  the 
tangle  was  at  length  unravelled  by  Duner,  of  Lund, 
who  showed  that  the  alternate  periods  were  unequal. 
The  intervals  between  minima  were  i  d.  Q  h.,  i  d. 
15  h.,  i  d,  9  h.,  i  d.  15  h.,  and  so  on,  indefinitely. 

This  law  once  established,  the  cause  of  the  anom- 
aly became  evident.  Two  bright  stars  revolve  round 
their  common  centre  of  gravity  in  a  period  of  nearly 
three  days.  Each  eclipses  the  other  in  alternation. 


no  VARIABLE  STARS 

The  orbit  is  eccentric,  and,  in  consequence,  one  half 
of  it  is  described  in  a  less  time  than  the  other  half. 
If  we  could  distinguish  the  two  stars  by  telescopic 
vision,  and  note  their  relative  positions  at  the  four 
cardinal  points  of  their  orbit,  we  should  see  the  pair 
alternately  single  and  double,  as  shown  in  the  follow- 
ing diagram  : 

A         B 

Position  ( i ),  stars  at  pericentre 

Interval,  16  hours. 

Position  (2),  A  eclipses  B * 

Interval  19  hours. 

B  A 

Position  (3),  stars  at  apocentre * 

Interval,  20  hours. 

Position  (4),  B  eclipses  A * 

Interval  17  hours. 

A          B 
Position  ( i )  is  repeated 

U  Pegasi  is  a  star  which  proved  as  perplexing  as 
Y  Cygni.  It  was  first  supposed  to  be  of  the  Algol 
type,  with  a  period  of  about  two  days.  Then  it  was 
found  that  a  number  of  minima  occurred  during  this 
period,  and  that  the  actual  interval  between  them  was 
only  a  few  hours.  The  great  difficulty  in  the  case  arises 
from  the  minuteness  of  the  variation,  which  is  but 
little  more  than  half  a  magnitude  between  the  ex- 
tremes. The  observations  of  Wendell,  at  the  Harvard 
Observatory,  with  the  polarising  photometer,  enabled 
Pickering  to  reach  a  conclusion  which,  though  it  may 
still  be  open  to  some  doubt,  seems  to  be  the  most 
likely  yet  attainable.  The  star  is  of  the  Beta  Lyrse 


THE  BETA  LYR&  TYPE 


type;  its  complete  period  is  8  hours  59  minutes  41 
seconds,  or  19  seconds  less  than  9  hours  ;  during- 
this  period  it  passes  through  two  equal  maxima,  each 
of  magnitude  9.3,  and  two  unequal  minima,  9.76  and 
9.9,  alternately. 


o"     r* 


9.2 

,§9.3 
59.4 
5  9.5 
•-9.6 

I97 
§9.8 

^9.9 
10.0 

S* 

""    X 

/ 

s^ 

N 

/ 

\ 

/ 

\ 

/ 

\ 

/ 

\ 

/ 

s    / 

\ 

/ 

v/ 

\ 

1 

\ 

LIGHT-CURVE  OF  U  PEQASI,  OF  THE  BETA  LYR/E  TYPE. 

The  difference  of  brightness  of  these  minima,  0.14 
mag.,  is  less  than  the  errors  which  ordinarily  affect  meas- 
ures of  a  star's  magnitude  with  the  best  photometers. 
Some  scepticism  has,  therefore,  been  felt  as  to  the 
reality  of  the  difference  ;  which,  if  it  does  not  exist, 
would  reduce  the  periodic  time  below  4-^-  hours,  the 
shortest  yet  known.  But  Pickering  holds  that,  in 
observations  of  this  kind  upon  a  single  star,  the 
precision  is  such  that  the  reality  of  the  difference, 
small  though  it  be,  is  beyond  serious  doubt. 

Taking  Pickering's  law  of  change  as  a  basis,  Myers 
has  represented  the  light-curve  of  U  Pegasi  on  a 
theory  similar  to  that  which  he  constructed  for  Beta 
Lyrse.  His  conclusion  is  that,  in  the  present  case,  the 
two  bodies  which  form  the  visible  star  are  in  actual 
contact.  A  remarkable  historic  feature  of  the  case  is 


ii2        .  VARIABLE  STARS 

that  Poincare  has  recently  investigated,  by  purely 
mathematical  methods,  the  possible  forms  of  revolving 
fluid  masses  in  a  condition  of  equilibrium,  bringing  out 
a  number  of  such  forms  previously  unknown.  One  of 
these,  which  he  calls  the  apioidal  form,  consists  of  two 
bodies  joined  into  one,  and  it  is  this  which  Myers 
finds  for  U  Pegasi. 

Quite  similar  to  these  two  cases  is  that  of  Z 
Herculis.  This  star,  ordinarily  of  the  seventh  mag- 
nitude, was  found,  at  Potsdam,  in  1894,  to  diminish 
by  about  one  magnitude.  Repeated  observations 
elsewhere  indicate  a  period  of  very  nearly  four  days. 
Actually  it  is  now  found  to  be  only  ten  minutes  less 
than  four  days.  The  result  was  that  during  any  one 
season  of  observation  the  minima  occur  at  nearly  the 
same  hour  every  night  or  day.  To  an  observer 
situated  in  such  longitude  that  they  occur  during  the 
day,  they  would,  of  course,  be  invisible. 

Continued  observations  then  showed  a  secondary 
minimum,  occurring  about  half-way  between  the 
principal  minima  hitherto  observed.  It  was  then 
found  that  these  secondary  minima  really  occur  some 
two  hours  earlier  than  the  mid-moment,  so  that  the  one 
interval  would  be  between  forty-six  and  forty-seven 
hours  and  the  other  between  forty-nine  and  fifty. 
The  time  which  it  takes  the  star  to  lose  its  light  and 
regain  it  again  is  about  ten  hours.  More  recent  ob- 
servations, however,  do  not  show  this  inequality,  so 
that  there  is  probably  a  rapid  motion  of  the  pericentre 
of  the  orbit. 

It  will  be  seen  that  this  star  combines  the  Algol 


THE  BETA  LYR^E  TYPE  113 

and  Beta  Lyne  types.  It  is  an  Algol  star  in  that  its 
light  remains  constant  between  the  eclipses.  It  is  of  the 
Beta  Lyrse  type  in  the  alternate  minima  being  unequal. 
Duner  subjected  the  observations  of  this  star  to  a  very 
careful  discussion.  His  conclusion  is  as  follows  : 

Z  Herculis  consists  of  two  stars  of  equal  size,  one  of  which  is 
twice  as  bright  as  the  other.  These  stars  revolve  around  their 
common  centre  of  gravity  in  an  elliptic  orbit  whose  semiaxis 
major  is  six  times  the  diameter  of  the  stars.  The  plane  of  the 
orbit  passes  through  the  sun  ;  the  eccentricity  is  0.2475,  and  the 
line  of  apsides  is  inclined  at  an  angle  of  4°  to  the  line  of  sight 
(Astrophysical  Journal,  vol.  i.). 

From  a  careful  study,  Seeliger  and  Hartwig  derived 
the  following  particulars  respecting  this  system : 

Diameter  of  principal  star,  15,000,000  kilometres. 

smaller       "       12,000,000         " 
Mass  of  the  larger  star,  172  times  sun's  mass. 
Mass  of  the  smaller  star,  84  times  sun's  mass. 
Distance  of  centres,  45,000,000  kilometres. 
Time  of  revolution,  3  d.  23  h.  49  m.  32.7  s. 

It  must  be  added  that  the  data  for  these  extra- 
ordinary numbers  are  rather  slender  and  partly 
hypothetical. 

Beta  Lyrse  is  always  of  the  same  brightness  at  the 
same  hour  of  its  period,  and  Algol  has  always  the 
same  magnitude  at  minimum.  It  is  true  that  the  length 
of  the  period  varies  slowly  in  the  case  of  these  stars. 
But  this  may  arise  from  the  action  of  other  invisible 
bodies  revolving  around  the  visible  stars.  This  general 
uniformity  is  in  accord  with  the  theory  which  attributes 
the  apparent  variations  to  the  various  aspects  in  which 
we  see  one  and  the  same  pair  of  revolving  stars. 


ii4  VARIABLE  STARS 

Another  variable  star  showing  some  unique  features 
is  Eta  Aquilse.  What  gives  it  special  interest  is  that 
Variation  of  spectroscopic  observations  of  its  radial  mo- 
Eta  Aquilae.  tion  show  it  to  have  a  dark  body  revolving 
round  it  in  a  very  eccentric  orbit,  and  in  the  same 
time  as  the  period  of  variation.  It  might  therefore  be 
supposed  that  we  have  here  a  star  of  the  Algol  or 
Beta  Lyrse  type.  But  such  is  not  the  case.  There  is 
nothing  in  the  law  of  variation  to  suggest  an  eclipsing 
of  the  bright  star,  nor  does  it  seem  that  the  variations 
can  readily  be  represented  by  the  varying  aspects  of 
any  revolving  system. 

The  orbit  of  this  star  has  been  exhaustively  investi- 
gated by  Wright  from  Campbell's  observations  of  the 
radial  motion.  The  laws  of  change  in  the  system  are 
shown  by  the  curves  below,  which  are  reproduced,  in 
great  part,  from  Wright's  paper  in  the  Astropkysical 
Journal. 


-H5 
+  /0 


Covj 


^ 


\ 


t-fm 


LIGHT-  AND  VELOCITY-CURVES  OF  1  AQUILXE  COMPARED. 


RADIAL  MOTIONS  115 

The  lower  curve  is  the  light-curve  of  the  star  during 
a  period  of  7.167  days.  Starting  from  a  maximum 
of  3.5  mag.,  it  sinks,  in  the  course  of  5  days,  to  a 
minimum  of  4.7  m.  It  was  found  by  Schwab  that  the 
diminution  is  not  progressive,  but  that  a  secondary 
maximum  of  3.8  m.  is  reached  at  the  end  of  the  second 
day.  After  reaching  the  principal  minimum  it  rises 
rapidly  to  the  principal  maximum  in  2\  days. 

The  upper  curve  shows  the  radial  velocity  of  the 
star  during  the  period  of  variation.  It  will  be  seen 
that  the  epoch  of  greatest  negative  velocity,  which,  re- 
ferred to  the  centre  of  mass  of  the  system,  is  16.2  km. 
per  second,  occurs  at  the  time  of  maximum  brightness. 
The  greatest  positive  velocity,  23.9  km.,  occurs  during 
the  sixth  day  of  the  period,  just  after  the  time  of 
minimum  brightness. 

Finally,  the  moments  of  inferior  and  superior  con- 
junction of  the  dark  body  with  the  bright  one  are 
neither  of  them  an  epoch  of  minimum  brightness, 
which  takes  place  half-way  between  the  two. 

The  case  of  Delta  Cephei  is  not  dissimilar  to  that 
of  Eta  Aquilae.  This  star  is  regularly  variable  in  a 
period  of  5.366  days.  Its  magnitude  at  maximum 
is  3.7  ;  at  minimum  4.9.  It  was  found  by  Belopolsky 
to  be  a  spectroscopic  binary  with  a  period  the 
same  as  that  of  its  variation  of  the  light.  He  finds 
that,  as  in  the  case  of  the  other  star,  there  appears 
to  be  nothing  in  the  nature  of  an  eclipse.  The 
orbit  is,  however,  very  eccentric.  The  epoch  of 
minimum  is  one  day  earlier  than  that  of  perihelion 
passage. 


u6  VARIABLE  STARS 

Its  slight  variation,  as  in  the  case  of  Eta  Aquilae,  is 
much  more  rapid  during  the  increase  than  during  the 
decrease.  From  Schur's  table  it  seems  that  the  whole 
time  of  rise,  from  minimum  to  maximum,  is  1.6  d., 
which  is  less  than  one-third  the  entire  period.  More- 
over, the  larger  part  of  this  change  takes  place  in  less 
than  a  day. 

A  classification  of  variable  stars,  based  on  the 
period  of  variation  and  the  law  of  change,  was  pro- 
Classifica-  posed  by  Pickering.  It  does  not,  however, 
tionofVari-  seem  that  a  hard-and-fast  line  can  yet  be 
able  Stars.  drawn  between  different  types  and  classes 
of  these  bodies,  one  type  running  into  angther,  as  we 
have  found  in  the  case  of  the  Algol  and  Beta  Lyrse 
types.  Yet  the  discovery  of  the  cause  of  the  variation 
in  these  types  makes  it  likely  that  a  division  into  four 
great  classes,  dependent  on  the  cause  of  variation,  is 
possible.  These  classes  are  : 

(i)  Stars,  or  systems  appearing  to  us  as  a  single 
star,  of  which  the  apparent  variability  arises  solely  or 
mainly  from  the  rotation  of  the  system  as  a  whole,  or 
from  the  revolution  of  its  components  around  each 
other.  In  this  case  the  variations  of  light  are  purely 
the  effect  of  perspective,  arising  from  the  various  as- 
pects which  the  system  presents  to  us  during  the 
revolution  of  its  components.  There  is  no  real  varia- 
tion either  in  the  constitution  of  the  star  or  in  the 
actual  amount  of  light  which  it  emits.  If  we  could 
change  our  point  of  view  so  that  the  plane  of  the  orbit 
of  an  Algol  star  no  longer  passed  near  our  system,  the 
star  would  cease  to  appear  variable.  Under  the  same 


C LA-SSI  PICA  TION  1 1 7 

circumstances  the  apparent  variations  of  a  star  of  the 
Beta  Lyrae  type  would  be  smaller  than  they  are,  and 
would  disappear  entirely  if  the  axis  of  rotation  were 
directed  toward  our  system.  The  stars  of  this  class 
are  also  distinguished  by  the  uniformity  and  regularity 
with  which  they  go  through  their  cycle  of  change. 

(2)  The  second  class  comprises  stars  in  which  the 
changes  of  light  are  real  and  arise  from  some  cycle  of 
change  going  on  in  the  star,  but  which  may  be  due  to 
the  action  of  an  external  body.  This  class  may  be 
divided  into  two  or  three  subclasses,  as  has  been  done 
by  Pickering,  depending  on  the  length  of  the  period 
and  the  character  of  the  variation.  But  it  does  not 
appear  that  we  can  yet  sharply  define  the  subdivision, 
because,  as  already  stated,  one  class  runs  into  the 
other  by  insensible  gradations.  Perhaps  the  best  de- 
fined class  is  that  of  the  Omicron  Ceti  type.  There 
are  certain  general  laws  of  variation  and  irregu- 
larities of  brightness  which  stars  of  this  class  go 
through.  Starting  from  the  time  of  the  minimum,  the 
increase  of  light  is  at  first  very  slow.  It  grows  more 
and  more  rapid  as  the  maximum  is  approached,  near 
which  there  may  be  as  great  an  increase  in  two  or  three 
days  as  there  formerly  was  in  a  month.  The  diminu- 
tion of  light  is  generally  slower  than  the  increase.  The 
magnitude  at  corresponding  times  in  different  periods 
may  be  very  different.  Thus,  as  we  have  already-re- 
marked, Omicron  Ceti  is  ten  times  as  bright  at  some 
maxima  as  it  is  at  others.  The  periods  also,  so  far  as 
they  have  been  made  out,  vary  more  widely  than  those 
of  stars  of  the  other  types.  The  most  remarkable 


u8  VARIABLE  STARS 

feature  of  this  type  is  found  in  its  spectrum.  Nearly 
all  these  stars  have  spectra  of  the  third  type  in  which 
the  hydrogen  lines  are  bright  at  the  time  of  maximum. 
So  well  defined  is  this  peculiarity  that  stars  are 
recognised  as  variable  at  the  Harvard  Observatory 
merely  by  this  feature  of  the  spectrum. 

From  what  has  been  said,  it  will  be  seen  that,  al- 
though a  sharp  line  cannot  be  drawn,  there  seems  to 
be  some  distinction  between  the  stars  of  short  and 
long  periods.  The  number  of  stars  which  have  been 
known  to  belong  to  the  first  class  is  quite  small,  only 
about  fifteen  all  told.  On  the  other  hand,  there  are 
still  left  some  stars  having  a  period  less  than  ten  days, 
which  are  otherwise  not  distinguishable  from  the 
Omicron  Ceti  type. 

The  discovery  that  Delta  Cephei  and  Eta  Aquilae 
have  dark  bodies  revolving  around,  them  in  a  period 
equal  to  that  of  the  variation  of  light,  suggests  the 
idea  that  in  perhaps  all  this  class  of  stars  the  variations 
of  light  are  due  to  the  varying  action  of  a  revolving 
planet  as  it  moves  around  in  a  very  eccentric  orbit. 

The  periodic  stars  of  short  period  which  have  not 
been  recognised  as  of  the  Algol  or  Beta  Lyrae  type 
form  an  interesting  subject  of  study.  Although  the 
separation  between  them  and  the  stars  of  long  period 
is  not  sharp,  it  seems  likely  to  have  some  element  of 
reality  in  it.  But  no  conclusions  on  the  subject  can 
be  reached  until  the  light-curves  of  a  large  number  of 
them  are  carefully  drawn ;  and  this  requires  an 
amount  of  patient  and  accurate  observation  which  can- 
not be  carried  out  for  years  to  come. 


SPECTRA  119 

(3)  The  third  class  comprises  stars  subject  to  small 
and  irregular  but  frequently  recurring  fluctuations  of 
light.      The   range  of  variation  is  commonly  only  a 
fraction  of  a  magnitude.     The  following  are  the  most 
noteworthy  examples  of  this  class  : 

a  Cassiopeae,  range  in  mag.  2.2  to  2.8 
p  Persei,  "  "  "  3.4  "  4.2 

arOrionis,  "  "  "  i.o  "  1.4 
a  Herculis,  "  "  "  4.6  "  5.4 
I*  Cephei,  "  "  "  4.0  "  5.0 
ft  Pegasi,  2.2  "  2.7 

(4)  The  fourth  class  are  the  "  novae,"  or  new  stars, 
which,  so  far  as  is  known,  blaze  out  but  once  in  history. 
They  will  be  described  in  the  next  chapter. 

It  might  be  supposed  that  the  changes  in  the  light 
of  the  variable  stars,  at  least  in  those  cases  where  they 
are  not  caused  by  a  mere  partial  eclipsing  spectra 
of  the  star,  would  be  accompanied  by  wide  of  Variable 
changes  in  their  spectra,  following  some  de-  stars, 

finable  law.  Many  studies  have  been  made  on  this 
subject,  but  it  is  difficult  to  formulate  any  general  con- 
clusion from  them.  The  investigation  is  a  difficult  one, 
because  the  most  interesting  cases  are  those  in  which 
the  diminution  of  light  at  minimum  is  very  great,  and 
the  spectrum  cannot  be  well  studied.  The  star  Omi- 
cron  Ceti  has  perhaps  been  more  carefully  studied  from 
this  point  of  view  than  any  other.  Campbell  found  that 
near  the  time  of  maximum,  the  bright  hydrogen  line 
Hr  was  very  strong  and  overexposed  on  all  the 
plates.  He  found  that  two  minutes  sufficed  to  obtain 
an  impression  of  this  line,  at  a  stage  of  brightness 


VARIABLE  STARS 


when  an  hour  is  wanted  for  the  rest  of  the  spectrum. 
Under  the  same  circumstances,  the  line  Htf  is  triple. 
The  central  component  of  this  triple  system  is  much 
stronger  than  the  two  others,  which  are  about  equal. 
As  the  spectrum  grows  fainter,  the  components 
occupy  nearly  the  position  of  certain  iron  lines,  but 
nothing  definite  can  be  ascertained  about  them. 


1897 
NOV.  29 


DEC.  11 


DEC.  19 


SPECTRUM  OF  O  CETI  NEAR  THE  MAXIMUM  OF  1897,  PHOTOGRAPHED  EY  FATHER 
SIDGREAVES  AT  THE  STONYHURST  COLLEGE  OBSERVATORY. 

The  question  whether  certain  stars  vary  in  colour 
without  materially  changing  their  brightness  has  some- 
Suspected  times  been  raised.  This  was  at  one  time 

Variations  supposecj  to  be  the  case  w}th  one  of  the 
in  the  Colour 

of  stars.  stars  of  Ursa  Major.  This  suspected  vari- 
ation has  not,  however,  been  confirmed,  and  it  does 
not  seem  likely  that  any  such  changes  take  place  in 
the  colour  of  stars  not  otherwise  variable. 


CHANGES  OF  COLOUR  121 

All  the  variations  we  have  hitherto  considered  take 
place  with  such  rapidity  that  they  can  be  observed  by 
comparisons  embracing-  but  a  short  interval  ,. 

e    .  ,          ,  ,  Possible  Sc- 

ot time — a  tew  days  or  months  at  the  out-  cuiar  Varia- 

side.  A  somewhat  different  question  of  tionf  in  the 
great  importance  is  still  left  open.  May  not  "f  stars* 
individual  stars  be  subject  to  a  slow  varia- 
tion either  in  their  colour  or  their  brightness,  which  are 
sensible  in  the  course  of  only  one  generation  of  men, 
but  admit  of  being  brought  out  by  a  comparison  of  the 
brightness  of  the  stars  at  widely  distant  epochs  ?  Is 
it  certain  that,  in  the  case  of  stars  which  we  do  not 
recognise  as  variable,  no  change  has  taken  place  since 
the  time  of  Hipparchus  and  Ptolemy  ?  This  question 
has  been  investigated  by  C.  S.  Pierce  and  others. 
The  conclusion  reached  is  that  no  real  evidence  of  any 
change  can  be  gathered.  The  discrepancies  are  no 
greater  than  might  arise  from  errors  of  estimates. 

There  is,  however,  an  aspect  of  the  question  which  is 
of  great  interest  and  has  been  much  discussed  in  re- 
cent times.  In  several  ancient  writings  the  colour  of 
Sirius  is  described  as  red.  This  fact  would,  at  first 
sight,  appear  to  afford  very  strong  evidence  that, 
within  historic  times,  the  colour  of  the  brightest  star  in 
the  heavens  has  actually  changed  from  red  to  bluish 
white. 

Two  recent  writers  have  examined  the  evidence  on 
this  subject  most  exhaustively  and  reached  opposite 
conclusions.  The  first  of  these  was  Prof.  T.  J.  J. 
See,  who  collated  a  great  number  of  cases  in  which 
Sirius  was  mentioned  by  ancient  writers  as  red  or  fiery, 


722  VARIABLE  STARS 

and  thus  concluded  that  the  evidence  was  in  favour  of 
a  red  colour  in  former  times.  Shortly  afterwards, 
Schiaparelli  examined  the  evidence  with  equal  care 
and  thoroughness  and  reached  an  opposite  conclusion, 
showing  that  the  terms  used  by  the  ancient  authors 
which  might  have  indicated  redness  of  colour  were 
susceptible  of  other  interpretations  ;  they  might  mean 
fiery,  blazing,  etc.,  as  well  as  red  in  colour,  and  were 
therefore  probably  suggested  by  the  extraordinary 
brightness  of  Sirius  and  the  strangeness  with  which  it 
twinkled  when  near  the  horizon.  In  this  position  a 
star  not  only  twinkles,  but  changes  its  colour  rapidly. 
This  change  is  not  sensible  in  the  case  of  a  faint  star, 
but  if  one  watches  Sirius  when  on  the  horizon,  it  will 
be  seen  that  it  not  only  changes  in  appearance,  but 
seems  to  blaze  forth  in  different  colours. 

It  seems  to  the  writer  that  this  conclusion  of 
Schiaparelli  is  the  more  likely  of  the  two.  From  what 
we  know  of  the  constitution  of  the  stars,  a  change  in 
the  colour  of  one  of  these  bodies  in  so  short  a  period  of 
time  as  that  embraced  by  history  is  so  improbable  as 
to  require  much  stronger  proofs  than  any  that  can  be 
adduced  from  ancient  writers.  In  addition  to  the 
possible  vagueness  or  errors  of  the  original  writers, 
we  have  to  bear  in  mind  the  possible  mistakes  or 
misinterpretations  of  the  copyists  who  reproduced 
the  manuscripts. 


CHAPTER  VIII 

NEW  STARS 

It  may  be  glorious  to  write 

Thoughts  that  shall  glad  the  two  or  three 

High  souls,  like  those  far  stars  that  come  in  sight 

Once  in  a  century.— LOWELL 

THE  stars  considered  in  the  preceding  chapter  go 
through  their  changes  of  light  in  a  limited  and 
generally  more  or  less  regular  period,  so  that  a  predic- 
tion of  their  brightness  at  future  epochs  is  in  most 
cases  possible.  They  are  distinguished  by  the  re- 
markable fact,  pointed  out  at  the  beginning  of  the 
chapter,  that  the  period  seems  to  be  limited,  none  so 
long  as  two  years  being  yet  known. 

New  stars,  or  "  Novse "  as  they  are  frequently 
called,  are  distinguished  from  the  irregularly  variable 
stars  already  described  by  their  blazing  forth,  so  far 
as  is  yet  known,  only  once  in  the  period  of  their  his- 
tory. 

The  limitation  of  the  period  seems  to  form  a  well- 
marked  distinction  between  periodic  stars  and  trie 
irregularly  variable  ones  now  to  be  considered,  and 
to  indicate  some  radical  difference  in  the  cause  of 
variability. 

123 


i24  NEW  STARS 

The  most  remarkable  among  these  stars  is  un- 
doubtedly Eta  Argus,  which,  though  now  invisible  to 
the  naked  eye,  was,  at  various  times  between  1830  and 
1850,  of  the  first  magnitude.  It  falls  so  closely  on  a 
line  between  the  new  or  temporary  stars  and  those 
which  are  irregularly  variable  that  it  may  form  a 
distinct  class.  Being  in  58°  of  south  declination  it 
is  not  visible  except  in  latitudes  south  of  32°.  For 
this  reason  it  could  not  be  made  a  subject  of  ob- 
servation in  northern  European  countries.  Of  the 
greatest  interest  is  the  question  whether  it  was 
visible  in  early  historic  times.  On  this  question  no 
decisive  evidence  can  be  gathered.  The  catalogues 
of  Ptolemy  and  Ulugh  Beigh  are  among  the  earlier 
authorities  which  we  consult  on  the  subject.  Much 
confusion,  however,  is  found  in  the  data  to  be  consult- 
ed. In  Halma's  edition  of  Ptolemy 's  catalogue,  two 
stars  in  the  constellation  Argo  are  marked  as  having 
the  Bayer  letter  Eta.  But  neither  of  these  is  near  the 
position  of  the  star  under  consideration.  In  fact, 
Ptolemy's  constell£tion  Argo  seems  scarcely  to  ex- 
tend as  far  east  as  the  point  in  question.  The  same 
remark  applies  to  the  mediaeval  catalogue  of  Ulugh 
Beigh.  The  only  conclusion  we  can  draw  on  the 
subject  is  that  the  star  was  probably  not  so  conspicu- 
ous in  early  historic  times  as  to  excite  the  attention 
of  observers. 

On  Bayer's  charts,  published  about  1600,  there  is 
a  star  marked  Eta,  but  this  is  nowhere  near  the  place 
of  the  modern  Eta,  nor  is  there  any  star  shown  in  the 
position  of  the  latter.  The  fact  appears  to  be  that 


ETA  ARGUS  125 

Bayer's  maps  of  this  constellation  are  so  erroneous  that 
little  correspondence  can  be  found  between  his  figures 
and  the  heavens,  and  the  certain  identification  of  any 
particular  star  scarcely  seems  possible,  except  in  the 
case  of  Canopus  and  possibly  a  few  other  bright  ones. 
Near  the  position  of  the  modern  Eta  are  several  small 
stars  marked  d,  but  from  what  has  been  said  we  have 
no  reason  to  identify  these  with  the  star  in  question. 
The  first  authentic  observation  of  the  star  is  found 
in  Halley's  catalogue,  made  at  St.  Helena  in  1677, 
where  it  appears  as  of  the  fourth  magnitude.  The  next 
observation  is  by  Lacaille,  who  observed  it  at  the  Cape 
of  Good  Hope  about  1750.  In  the  catalogue  at  the 
end  of  his  Calum  Australe  Stelliferum,  the  star  is 
given  as  of  the  second  magnitude  ;  but  in  the  original 
observations  it  is  marked  of  magnitude  2.3.  It  may 
be  added  that  Lacaille  was  the  first  one  to  assign 
the  symbol  Eta.  From  a  remark  at  the  end  of  the 
catalogue,  it  seems  that  he  assigned  these  symbols  in 
accordance  with  Bayer  only  when  the  Bayer  stars 
could  be  identified,  but  it  would  seem  that  there 
could  have  been  few  such  identifications  in  Argo.  In 
catalogues  made  between  the  years  1822  and  1832 
it  still  appears  as  of  the  second  magnitude ;  whether 
this  magnitude  was  an  independent  one  or  merely 
taken  from  Lacaille  may  be  an  open  question,  but 
we  cannot  suppose  that  the  variation  from  Lacaille's 
estimate  was  at  all  striking.  A  traveller  named 
Birchell  noted  it  as  of  the  first  magnitude  in  1827, 
but  this  seems  doubtful  in  view  of  the  records  of 
other  observers. 


126  NEW  STARS 

Our  next  authority  on  the  subject  is  Sir  John 
Herschel,  who,  during  his  residence  at  the  Cape  of 
Good  Hope,  in  1834,  noted  Eta  Argus  as  of  mag- 
nitude between  first  and  second.  It  remained  with- 
out exciting  any  suspicion  of  change  to  near  the  end 
of  1837.  In  December  of  this  year  Herschel's  as- 
tonishment was  excited  by  the  appearance  of  "  a  new 
candidate  for  distinction  among  the  very  bright  stars 
of  the  first  magnitude,  in  a  part  of  the  heavens  with 
which  being  perfectly  familiar,  I  was  certain  that  no 
such  brilliant  object  had  before  been  seen."  This  was 
soon  found  to  be  identical  with  Eta  Argus,  of  which  the 
light  had  nearly  trebled.  It  decidedly  surpassed  Pro- 
cyon,  Alpha  Orionis,  and  even  Rigel,  which  was  nearest 
to  it.  It  continued  to  increase  until  the  beginning  of 
January,  1838,  when  it  was  equal  to  Alpha  Centauri. 
Then  it  began  slowly  to  fade,  but  on  April  i/j-th,  which 
seems  to  have  been  the  date  of  Herschel's  last  observa- 
tion, it  was  still  about  equal  to  Aldebaran,  and  therefore 
of  the  first  magnitude.  It  seems  to  have  blazed  up 
again,  according  to  the  testimony  of  observers,  in 
1843,  when  it  was  fully  as  bright  as  Canopus,  and 
could  not  therefore  have  been  far  below  Sirius.  It 
fluctuated  during  the  following  ten  years,  and  then 
began  to  fade  away  slowly.  In  1868  it  was  estimated 
by  Mr.  Tebbut  as  only  of  the  sixth  magnitude,  and 
gradually  disappeared  from  vision  by  the  naked  eye 
in  the  year  following.  During  the  last  fifteen  or 
twenty  years  it  has  generally  been  of  the  seventh 
magnitude,  or  fainter,  and  there  is  no  evidence  of  any 
approaching  renewal  of  its  bright  stage  of  half  a 


NEW  STARS  127 

century  ago.  I  quote  the  following  list  of  deter- 
minations  from  Mr.  R.  T.  A.  Innes  (M.  N.  R.  A.  SM 
lix.,  570.) 

Year  1886.  2 Mag.  7.60  (Finlay) 

1896.4 "  7.58  (Innes) 

1897.2 "  7.60  (See) 

1899.5 "  7-71  (Innes) 

We  now  pass  to  the  class  of  new  or  temporary 
stars  properly  so  called.  A  distinguishing  feature  of 
a  star  of  this  class  is  that  it  blazes  up,  so  far  as  is 
known,  only  once  in  the  period  of  its  history,  then 
gradually  fades  away  to  its  former  magnitude,  which 
it  commonly  retains  with,  so  far  as  is  yet  known, 
little  or  no  subsequent  variation. 

It  was  formerly  supposed  that  stars  of  this  class 
were  new  creations  which  went  out  of  existence  after 
a  span  of  life  which  would  have  been  brief  even  for 
a  human  being,  much  less  for  a  star.  It  is  hardly 
necessary  to  say  that  such  a  view  as  this  can  find 
no  place  in  modern  science. 

Miss  Clerke,  in  her  System  of  the  Stars,  gives  a  list 
of  ten  such  stars  which  appeared  between  B.C.  134 
and  the  end  of  the  fifteenth  century.  Accepting  all 
these  as  real  there  would  be  an  average  of  one  such 
star  in  about  160  years.  In  the  few  cases  where 
the  duration  of  the  appearance  is  given  it  varies 
from  three  weeks  to  eight  months.  The  following 
list  of  such  stars  which  have  appeared  since  1500 
is  compiled  from  the  circulars  of  the  Harvard  Ob- 
servatory : 


128 


NEW  STARS. 


YEAR. 

CONSTELLA- 
TION. 

POSITION,  1900. 

MAG. 

DISCOVERER. 

R.  A. 

DEC. 

H.   M. 

T572- 

Cassiopeia. 

0.19.2 

+63°  36' 

Br. 

Tycho. 

1600. 

Cygnus. 

20.I4.I 

+37    43 

3 

Janson. 

1604. 

Ophiuchus. 

17.24.6 

—  21      24 

Br. 

Kepler. 

1670. 

Vulpecula. 

I9-43-5 

+  27      4 

3 

Anthelm. 

1848. 

Ophiuchus. 

16.53-9 

—12    44 

5 

Hind. 

1860. 

Scorpius. 

16.11.1 

—  22    44 

7 

Auwers. 

1866. 

Corona  Bor  . 

iS-55-3 

+  26      12 

2 

Birmingham. 

1876. 

Cygnus. 

21.37.8 

+42  23 

3 

Schmidt. 

1885 

Andromeda. 

0.37.2 

+40   43 

7 

Hartwig. 

1887. 

Perseus. 

I-55-1 

+56    15 

9 

Fleming. 

1891. 

Auriga. 

5-25-6 

+  3°     22 

4 

Anderson. 

1893. 

Norma. 

15.22.2 

—50     14 

7 

Fleming. 

1895. 

Carina. 

ii.  3.9 

—  6  1    24 

8 

Fleming. 

1895. 

Centaurus. 

13-34-3 

-3i      8 

7 

Fleming. 

1898. 

Sagittarius. 

18.56.2 

-13      8 

5 

Fleming. 

1901  . 

Perseus. 

3.22 

+44      o 

0 

Anderson. 

Among  all  these  the  first,  sometimes  called  Tycho's 
Star,  was  the  most  brilliant.  It  was  first  noticed  on  No- 
vember 7,  I572,1  by  Lindaeur  at  Winterthur.  It  was 
first  seen  by  Tycho  Brahe  four  days  later,  when  it 
had  attained  the  first  magnitude.  It  continued  to 
increase  in  brilliancy,  at  length  becoming  equal  to 
Venus  and  visible  in  full  daylight.  In  December  it 
began  to  diminish,  faded  gradually  away,  and  finally 
disappeared  from  view  in  May.  As  the  telescope 
was  then  unknown,  it  was  impossible  to  follow  it 
further. 

During  the  period  of  its  visibility  Tycho  not  only 
made  all  the  observations  he  was  able  to  on  its  ap- 
pearance, but  measured  its  position  relative  to 
other  stars.  It  is  now  found  that  a  star  of  magni- 

1  System  of  Stars,  page  97. 


NEW  STARS  129 

tude  10.5  is  situated  within  a  minute  of  the  posi- 
tion derived  from  Tycho's  observations.  In  view  of 
this  fact  there  is  a  strong  presumption  that  this  is 
the  star.  It  has  therefore  been  watched  occasionally 
to  detect  evidences  of  variability,  but,  although  some 
change  was  strongly  suspected  by  Hind,  it  does  not 
appear  that  observations  upon  it  have  been  made 
systematically  enough  to  establish  any  actual  change 
at  the  present  time. 

Of  Janson's  Star  of  1600  little  is  known;  a  star 
called  P  Cygni  is  supposed  to  be  identical  with  it,  but 
on  what  authority  I  do  not  know. 

The  star  of  1604  in  Ophiuchus  has  a  history  not 
unlike  that  of  Tycho.  It  was  first  seen  in  October, 
when  it  had  attained  the  first  magnitude.  In  a  few 
days  it  became  as  bright  as  Jupiter,  but  began  to  fall 
off  during  the  winter.  It  seems  to  have  been  re- 
markable for  its  duration,  having  been  visible  to  the 
naked  eye  during  the  whole  year  1605.  Early  in 
1606  it  disappeared  from  view.  A  very  full  history 
of  this  star  has  been  left  by  Kepler. 

Nearly  two  centuries  now  elapse  before  we  have 
any  record  of  another  appearance  of  the  kind.  On 
April  28,  1848,  Mr.  Hind,  then  in  charge  of  a  private 
observatory  in  London,  noticed  a  star  of  between  the 
fourth  and  fifth  magnitude  where  none  had  been 
seen  April  5th.  For  some  days  it  seems  to  have  fluctu- 
ated between  the  fifth  and  sixth  magnitudes.  Soon 
it  began  to  diminish  and  fade  away  year  after  year 
until  it  sank  to  magnitude  12.5,  at  which  it  seems  to 
have  remained  for  more  than  thirty  years. 


i3o  NEW  STARS 

The  Auwers  Star  of  1860  was  discovered  in  the 
cluster  Messier  80.  It  only  reached  the  seventh 
magnitude,  soon  faded  away,  and  has  not  since  been 
recognised.  It  is  mainly  of  interest  in  connection 
with  the  recent  discovery  at  the  Harvard  Observatory 
of  great  numbers  of  variable  stars  in  clusters. 

The  star  T  Coronse,  which  appeared  in  May,  1866, 
attained  the  greatest  brilliancy  of  any  new  star  since 
that  of  Kepler,  having  been  nearly  or  quite  of  the 
second  magnitude.  One  of  the  most  interesting 
questions  connected  with  it  is  the  rapidity  with  which 
such  a  star  may  blaze  up,  a  question  which  is  not  vet 
fully  settled.  The  facts  on  record  are  that  on  the 
1 2th  and  I3th  of  May  it  was  remarked  independently 
by  at  least  five  observers  in  Europe  and  America. 
On  May  12th  Schmidt  of  Athens,  who  was  scanning 
the  heavens,  asserts  in  the  most  positive  manner  that 
the  star  could  not  have  been  visible  without  his 
having  noticed  it.  If  we  accept  this  negative  testi- 
mony as  conclusive  the  star  must  have  risen  from 
some  low  magnitude,  probably  fainter  than  the  fifth, 
to  the  second,  within  a  few  hours. 

The  star  is  of  special  interest  as  the  first  of  which 
the  light  could  be  analysed  with  the  spectroscope. 
This  was  done  by  Mr.  Huggins  on  the  first  evening 
after  he  received  notice  of  the  strange  object.  He 
found  the  spectrum  to  be  a  singularly  composite  one, 
leading  to  the  conclusion  that  two  distinct  spectra 
were  superimposed,  and  that  the  light  had  emanated 
from  two  different  sources,  each  forming  its  own 
spectrum.  The  principal  spectrum  was  analogous 


NEW  STARS  131 

to  that  of  the  sun.  It  indicate4  light  emitted  by  an 
incandescent  photosphere  which  suffers  partial  ab- 
sorption by  passing  through  a  vaporous  atmosphere. 
Beginning  at  the  red  end  of  the  spectrum  the  first 
dark  line  was  a  little  more  refrangible  than  the  hydro- 
gen line  C.  Next  came  a  shaded  group  of  lines, 
then  a  faint  line  coincident  with  D.  In  the  higher 
regions  of  the  spectrum,  the  lines  were  stronger  and 
extended  as  far  as  the  spectrum  could  be  traced. 

The  second  spectrum  was  composed  of  five  bright 
lines.  One  of  these  seemed  to  coincide  with  line  C  ; 
still  brighter  was  one  coinciding  with  F,  then  two 
fainter  lines.  The  fifth  bright  line  was  near  G.  All 
the  bright  lines  were  much  more  apparent  than  the 
continuous  spectrum.  It  would  follow  that  the  gas 
which  emitted  them  must  have  had  a  temperature 
higher  than  that  of  the  stellar  photosphere  from 
which  the  light  forming  the  other  spectrum  emanated. 

Mr.  Muggins  compared  the  spectrum  of  the  star 
with  that  of  hydrogen.  It  seemed  quite  apparent 
that  two  of  the  brighter  lines  were  entirely  co- 
incident with  the  lines  C  and  F  of  hydrogen.  The 
conclusion,  therefore,  was  that  the  great  brilliancy  of 
the  star  was  due  to  an  outburst  of  incandescent 
hydrogen,  giving  rise  to  a  volume  of  flame  of  such 
magnitude  as  to  be  visible  at  the  vast  distance  of  our 
system. 

The  star  faded  away  with  great  rapidity.  In 
twelve  days  it  fell  from  the  second  to  the  eighth 
magnitude,  so  that  no  opportunity  was  afforded  for  a 
continuous  study  of  its  spectrum. 


i32  NEW  STARS 

The  stars  which  Ijave  subsequently  appeared  have 
naturally  been  studied  by  a  greater  number  of  ob- 
servers and  with  much  detail.  Among  them  Nova 
Aurigse,  which  appeared  in  February,  1892,  long 
held  the  first  place,  on  account  of  the  length  of  time 
during  which  it  remained  bright  enough  for  favourable 
examination.  A  citation  of  the  observations  and  re- 
searches would  fill  a  small  volume.  Within  our  limited 
space  we  can  only  summarise  the  principal  conclusions 
of  Campbell,  Sidgreaves,  and  Vogel. 

The  star  was  first  noticed  by  Dr.  Anderson,  a 
diligent  watcher  of  the  heavens,  at  Edinburgh  about 
the  end  of  January,  1892.  As  it  has  been  in  some 
noteworthy  cases  since,  the  region  occupied  by  the 
star  was  found  to  have  been  photographed  at  the 
Harvard  Observatory  before  the  star  was  noticed  by 
Dr.  Anderson.  On  November  2,  1891,  the  star  was 
not  shown  on  a  plate  where  those  of  the  eleventh  mag- 
nitude were  impressed.  On  December  ist  it  would 
have  been  shown  had  it  been  brighter  than  the  sixth 
magnitude.  The  first  plate  on  which  it  was  found 
bore  the  date  December  i6th,  when  the  magnitude 
was  the  sixth.  Two  days  previously  it  was  invisible 
on  a  plate  taken  at  a  European  observatory.  It  must 
therefore  have  blazed  up  within  a  period  of  two  or 
three  days.  It  seemed  to  vary  from  night  to  night  — 
at  least  the  magnitudes  assigned  by  the  observers 
were  very  different.  Early  in  March  it  began  to 
fade  rapidly.  By  the  middle  of  the  month  it  had 
sunk  to  the  eighth  magnitude,  and,  by  the  end,  to  the 
twelfth.  For  several  months  it  was  supposed  to 


NOVA  AURIGA  133 

have  sunk  almost  out  of  sight,  as  the  minutest  object 
visible  in  the  most  powerful  telescopes.  But  in 
August  new  interest  was  excited  by  its  again  blazing 
up  to  the  ninth  magnitude.  From  this  time  it  seems 
to  have  fluctuated  in  a  very  irregular  way  for  nearly 
a  year  before  it  finally  sunk  into  its  former  in- 
significance. 

Its  spectrum  was  of  course  photographed  by  every 
astronomer  who  had  the  means  of  doing  so.     Lock- 


SPECTRUM  OF  NOVA  AURIQ/E  PHOTOGRAPHED  BY  CAMPBELL 

yer  and  Huggins  in  England,  Vogel  in  Germany, 
and  Campbell  at  Mount  Hamilton  are  the  investi- 
gators on  whom  we  shall  mainly  depend.  Lockyer 
found  that  all  the  lines  in  the  spectrum  were  broad, 
although  they  showed  perfectly  sharp  in  the  spectrum 
of  Arcturus.  There  was  no  falling  off  of  intensity 
at  the  edges  of  the  bright  lines.  The  hydrogen  lines 
and  the  K  line  of  calcium  were  very  bright  and  accom- 
panied by  dark  lines  on  their  more  refrangible  sides. 
As  Campbell  had  the  best  optical  means  for  photo- 
graphing the  spectrum,  we  reproduce  one  of  his 


i34  NEW  STARS 

photographs,  taken  on  February  28th.  It  is  accom- 
panied by  an  intensity  curve,  showing  the  intensity  of 
the  light  in  the  various  parts  of  the  spectrum  by  the 
length  of  the  ordinate  with  greater  accuracy  than  it 
can  be  inferred  from  the  figure  of  the  spectrum.  The 
numbers  on  the  spectrum  are  the  wave-lengths  in 
millionths  of  a  millimetre. 

The  apparent  superposition  of  at  least  two  spectra, 
one  continuous  with  dark  lines,  the  other  consisting 
of  bright  lines,  was  noticed  both  by  Campbell  and 
Vogel.  The  latter  found  the  spectrum  to  extend  far 
into  the  violet,  showing  many  bright  and  broad  lines, 
among  which  the  whole  range  of  hydrogen  lines  were 
especially  noticeable ;  but  on  the  more  refrangible 
side  most  of  these  were  broad,  dark  lines,  whose 
distances  from  the  bright  lines  increased  in  going 
toward  the  violet  in  proportion  to  the  increasing 
dispersion  of  the  prism,  and  whose  identity  with  the 
bright  lines  is  thereby  established.  On  February 
2Oth  Vogel  compared  the  spectrum  with  that  of  hy- 
drogen, showing  with  seeming  certainty  that  this 
element  was  principally  concerned  in  forming  the 
spectrum.  The  main  difference  was  that  the  lines 
were  bright  in  the  spectrum  of  the  star  and  were  per- 
ceptibly brighter  and  more  sharply  defined  on  the 
side  toward  the  violet  than  on  that  toward  the  red. 
Besides  being  three  or  four  times  brighter  than  the 
lines  of  hydrogen,  they  were  displaced  strongly  toward 
the  red,  showing  a  rapid  motion  away  from  the  earth. 
On  the  other  end  the  dark  lines  which  accompanied 
the  bright  ones  were  so  much  displaced  toward  the 


NOVA  AURIG&  135 

violet  that  they  could  be  readily  distinguished.  A 
remarkable  fact  noticed  by  Vogel  was  that  a  number 
of  the  lines  coincided  with  those  of  the  sun's  chromo- 
sphere as  catalogued  by  Young. 

On  March  igth  the  continuous  spectrum  was  very 
faint  and  fell  off  rapidly  beyond  F.  The  latter  was 
now  the  brightest  line  in  the  spectrum,  but  several 
were  occasionally  glimpsed  in  the  green. 

After  the  star  again  brightened  up  in  September 
there  was  a  change  in  the  spectrum,  which  now  con- 
sisted principally  of  a  bright  line  in  the  green  and 
a  faint  continuous  spectrym.  This  continued. without 
change  until  March,  1893.  The  lines  coincided  with 
the  brighter  ones  in  the  spectrum  of  the  nebulse,  but 
there  was  also  a  very  faint  continuous  spectrum.  It 
was  noted  by  other  observers  that  the  spectrum  now 
became  identical  with  that  of  a  planetary  nebula. 

The  remarkable  opposite  displacement  of  the  lines 
during  the  early  period  of  the  star's  visibility  is  shown 
in  the  following  condensed  summary  of  the  results  of 
Vogel's  measures:  Taking  the  first  four  bright  lines 
of  hydrogen  and  calcium  the  following  velocities 
away  from  the  earth  were  derived  from  the  four 
lines : 

K 243  kilometres  per  second 

H 265 

HS 402 

Hv 457 

It  will  be  seen  that  the  calcium  lines  agree  fairly 
well  in  giving  a  motion  of  250  kilometres,  while  the 
hydrogen  lines,  especially  H  .  give  a  considerably 


136  NEW  STARS 

larger  motion,  the  mean  of  the  two  being  430  kilo- 
metres per  second. 

Very  different  was  it  with  the  accompanying  dark- 
line  spectrum.  The  two  hydrogen  lines  agreed  in 
giving  a  motion  toward  the  earth  of  about  780  kilo- 
metres per  second.  The  difference  of  these  two 
results  is  enormous,  more  than  600  English  miles 
per  second. 

The  problem  of  reconciling  these  rapid  motions 
with  any  easily  conceivable  constitution  of  the  body 
or  bodies  was  no  easy  one,  and  the  proposed  so- 
lutions can  hardly  be  considered  as  better  than 
speculations.  The  view  most  generally  received 
was  that  two  bodies  had  suddenly  approached  very 
closely  together,  perhaps  come  into  collision,  and 
then  separated.  While  this  view  is  by  no  means 
impossible,  it  is  far  from  being  established.  The 
great  change  in  the  character  of  the  spectrum,  while 
not  conclusive  against  it,  certainly  seems  to  throw 
difficulties  in  the  way  of  its  reception.  The  history 
of  the  star  leaves  us  in  great  doubt  on  the  question 
whether,  even  if  the  displacement  of  the  lines  was 
due  to  a  rapid  motion,  the  latter  was  the  integral 
motion  of  a  body.  It  might  have  been  only  that 
of  an  incandescent  gas  escaping  from  under  press- 
ure, in  a  direction  from  our  system,  in  fact,  an  erup- 
tion of  hydrogen  and  calcium  vapours.  If  these 
vapours,  after  cooling,  fell  back  again  in  such  a  way 
as  to  cut  off  the  light  of  the  brighter  region  be- 
yond, they  would  absorb  the  dark  lines  and  give  the 
spectrum  of  a  dark  body  moving  toward  us. 


CAUSE  OF  NEW  STARS  137 

The  most  recent  investigations  showing  to  what 
changes  the  form,  position,  and  brightness  of  spectral 
lines  are  subject  through  changes  in  the  physical 
condition  of  the  bodies  which  emit  the  light  lead  to 
great  caution  in  attributing  the  displacement  of 
broadened  lines  in  any  spectrum  to  motion. 

The  fact  that  these  objects  blaze  up  only  once 
in  their  history  shows  that  the  phenomenon  is  due 
to  some  cataclysm  of  a  rather  extraordinary  kind. 
The  first  and  most  interesting  question  raised  by  this 
fact  is  whether  one  star  is  more  likely  to  be  subject 
to  such  a  cataclysm  than  another.  If  new  stars  were 
known  to  vary,  or  to  have  any  special  kind  of  spec- 
trum before  their  sudden  outburst,  we  should  know 
that  the  latter  was  a  catastrophe  to  which  only  a 
particular  kind  of  star  is  subject.  If  we  could  find 
no  peculiarity  in  the  spectrum  of  the  star  we  should 
conclude  that  the  catastrophe  was  due  to  some  ex- 
ternal cause.  But  unfortunately  we  have  thus  far 
no  record  of  any  new  star  before  its  agpearance 
except,  in  a  very  few  cases,  its  position  in  the  heavens. 
It  is  true  that  the  star  may  be  studied  after  it  has 
settled  down  again,  but  if  the  catastrophe  was  due  to 
an  external  cause,  we  have  no  reason  to  suppose  that 
it  had  relapsed  to  its  former  condition.  Quite  likely 
the  cataclysm  might  have  made  a  permanent  change 
in  its  constitution. 

Perhaps  the  most  natural  theory  at  first  sight  is 
that  the  outburst  is  due  to  a  collision.  It  seems 
probable  that  stars  like  our  sun,  which  are  in  a  state 
of  considerable  condensation,  have  somewhat  the 


I38  NEW  STARS 

character  of  masses  of  gas  confined  under  enormous 
pressure,  as  if  they  were  hollow  globes  of  highly 
heated  and  compressed  gas.  We  do  not  mean  by  this 
that  the  shell  is  solid  ;  what  is  possible  is  that  it  is 
composed  of  divided  matter  probably  denser  than 
the  gases  below,  and  compressing  the  latter  by  its 
weight  rather  than  by  its  tension.  If,  by  the  fall  of 
a  foreign  body,  an  opening  is  suddenly  made  in  the 
shell,  the  interior  gases  will  burst  forth.  What  mag- 
nitude the  outburst  might  assume  it  is  impossible 
to  say,  and  cautious  thinkers  will  decline  to  accept 
this  or  any  other  solution  until  we  have  had  more  ex- 
perience on  the  subject. 

A  general  fact  that  seems  supported  by  the  most 
recent  observations  is  that  after  their  outbursts  of 
light  these  bodies  settle  down  to  a  nebular  condition. 
This  was  the  case  with  Nova  Aurigae,  and  the  recent 
Nova  Aquilse  of  1900.  Campbell  found  the  spec- 
trum of  the  latter  to  consist  of  extremely  faint  con- 
tinuous light  in  the  green,  and  three  bright  bands  in 
the  positions  of  the  three  nebular  lines. 

On  the  night  of  February  21-22,  1901,  Dr.  Ander- 
son of  Edinborough  noticed  a  previously  unknown 
The  New  star  °^  magnitude  2.7,  in  the  constellation 
star  of  1901  Perseus.  In  the  course  of  the  next  two 
seus<  days  it  increased  so  rapidly  as  to  become 
about  the  third  brightest  star  in  the  sky,  being  a 
little  brighter  than  Capella.  Then  it  began  slowly 
to  fade  away.  Early  in  March  it  was  again  of  the 
third  magnitude,  and  before  the  middle  of  April  had 
dropped  to  the  fifth. 


NOVA  PERSEI  139 

It  seems  to  have  blazed  out  with  extraordinary 
rapidity.  It  happened  most  fortunately  that  the 
region  had  been  photographed  at  the  Harvard  Ob- 
servatory several  times  during  the  month  of  Febru- 
ary, the  last  photograph  having  been  taken  on  the 
1 9th.  The  plate  showed  stars  as  faint  as  the  eleventh 
magnitude.  It  must  therefore  have  risen  from  some 
magnitude  below  the  eleventh  to  the  first  within 
about  three  days.  This  difference  corresponds  to  an 
increase  of  the  light  ten  thousandfold. 

Its  spectrum  shows  the  mixture  of  dark  and  bright 
bands  characteristic  of  new  stars.  But,  in  the  begin- 
ning, Campbell  found  that  the  sodium  lines  were  faint 
and  dark.  He  was  thus  enabled  to  determine  the 
radial  velocity  of  the  star,  which  was  six  kilometres 
per  second  away  from  the  sun. 

Nova  Persei,  as  the  star  will  hereafter  be  called,  is 
the  brightest  new  star  that  has  been  recorded  since 
the  time  of  Kepler.  But  it  is  not  impossible  that, 
before  the  heavens  were  so  carefully  watched  by  ob- 
servers, such  an  object  might  have  reached  an  equal 
degree  of  brightness  without  exciting  notice.  The 
complete  history  of  this  star  cannot  yet  be  written, 
and  there  is  no  reason  to  suppose  that  it  will  differ 
very  widely  from  that  of  Nova  Aurigie.  Indeed  on 
June  25,  1901  Professor  Pickering  reported  that  its 
spectrum  had  been  gradually  changing  into  that  of  a 
gaseous  nebula. 


CHAPTER    IX 

THE  PARALLAXES  OF  THE  STARS 

These  mathematic  men  have  thoughts  that  march 
From  sphere  to  sphere  and  measure  out  the  blue 
Of  infinite  space  like  roods  of  garden  ground. 

BLACKIE. 

IT  needs  only  the  most  elementary  conceptions  of 
space,  direction,  and  motion  to  see  that,  as  the 
earth  makes  its  vast  swing  from  one  extremity  of  its 
orbit  to  the  other,  the  stars,  being  fixed,  must  have  an 
apparent  swing  in  the  opposite  direction.  The  seem- 
ing absence  of  such  a  swing  was  in  all  ages  before  our 
own  one  of  the  great  stumbling-blocks  of  astronomy. 
It  was  the  base  on  which  Ptolemy  erected  his  proof 
that  the  earth  was  immovable  in  the  centre  of  the 
celestial  sphere.  It  was  felt  by  Copernicus  to  be  a 
great  difficulty  in  the  reception  of  his  system.  I  tied 
Tycho  Brahe  to  suggest  a  grotesque  combination  of 
the  Ptolemaic  and  Copernican  systems,  in  which  the 
earth  was  the  centre  of  motion,  round  which  the  sun 
revolved,  carrying  the  planets  with  it. 

With  every  improvement  in  their  instruments,  as- 
tronomers sought  to  detect  the  annual  swing  of  the 
stars.     Each  time  that  increased  accuracy  in  observa- 
140 


THE  PARALLAXES  OF  THE  STARS  141 

tions  failed  to  show  it,  the  difficulty  in  the  way  of  the 
Copernican  system  was  heightened.  How  deep  the 
feeling  on  the  subject  is  shown  by  the  enthusiastic 
title,  Copernicus  Triumphans,  given  by  Horrebow  to 
the  paper  in  which,  from  observations  by  Roemer,  he 
claimed  to  have  detected  the  swing.  But,  alas, 
critical  examination  showed  that  the  supposed  in- 
equality was  produced  by  the  varying  effect  of  the 
warmth  of  the  day  and  the  cold  of  the  night  upon 
the  rate  of  the  clock  used  by  the  observer,  and  not  by 
the  motion  of  the  earth. 

Hooke,  a  contemporary  of  Newton,  published  an 
attempt  to  determine  the  parallax  of  the  stars,  under 
the  title  An  Attempt  to  Prove  the  Motion  of  the  Earth, 
but  his  work  was  as  great  a  failure  as  that  of  his  pre- 
decessors. Had  it  not  been  that  the  proofs  of  the 
Copernican  system  had  accumulated  until  they  became 
irresistible,  these  repeated  attempts  might  have  led 
men  to  think  that  perhaps,  after  all,  Ptolemy  and  the 
ancients  were  somehow  in  the  right. 

The  difficulty  was  magnified  by  the  philosophic 
views  of  the  period.  It  was  supposed  that  Nature 
must  economise  in  the  use  of  space  as  farmer  would 
in  the  use  of  valuable  land.  The  ancient  astronomers 
correctly  placed  the  sphere  of  the  stars  outside  that  of 
the  planets,  but  did  not  suppose  it  far  outside.  That 
Nature  would  squander  her  resources  by  leaving^  a 
vacant  space  hundreds  of  thousands  of  times  the  ex- 
tent of  the  solar  system  was  supposed  contrary  to  all 
probability.  The  actual  infinity  of  space  ;  the  con- 
sideration, that  one  had  only  to  enlarge  his  conceptions 


142  THE  PARALLAXES  OF  THE  STARS 

a  little  to  see  spaces  a  thousand  times  the  size  of  the 
solar  system  look  as  insignificant  as  the  region  of  a 
few  yards  round  a  grain  of  sand,  does  not  seem  to 
have  occurred  to  anyone. 

Considerations  drawn  from  photometry  were  also 
lost  sight  of,  because  that  art  was  still  undeveloped. 
Kepler  saw  that  the  sun  might  well  be  of  the  nature  of 
a  star  ;  in  fact,  that  the  stars  were  probably  suns. 
Had  he  and  his  contemporaries  known  that  the  light  of 
the  sun  was  more  than  ten  thousand  million  times  that 
of  a  bright  star,  they  would  have  seen  that  if  placed 
at  one  hundred  thousand  times  its  present  distance 
the  sun  would  still  shine  as  a  bright  star.  If,  then,  the 
stars  are  as  bright  as  the  sun,  they  must  be  one  hun- 
dred thousand  times  as  far  away,  and  their  annual 
parallax  would  then  have  been  too  small  for  detection 
with  the  instruments  of  the  time.  Such  considerations 
as  this  would  have  removed  the  real  difficulty. 

The  efforts  to  discover  stellar  parallax  were,of  course, 
still  continued.  Bradley,  about  1 740,  made  observa- 
tions on  Gamma  Draconis,  which  passed  the  meridian 
near  his  zenith,  with  an  instrument  of  an  accuracy  be- 
fore unequalled.  He  thus  detected  an  annual  swing 
of  20"  on  each  side  of  the  mean.  But  this  swing  did 
not  have  the  right  phase  to  be  due  to  the  motion  of 
the  earth  ;  the  star  appeared  at  one  or  the  other  ex- 
tremity of  its  swing  when  it  should  have  been  at  the 
middle  point,  and  vice  versa.  What  he  saw  was  really 
the  effect  of  aberration,  (depending  on  the  ratio  of  the 
velocity  of  the  earth  in  its  orbit  to  the  velocity  of  light. 
It  proved  the  motion  of  the  earth,  but  in  a  different 


FIRST  MEASURES  OF  PARALLAX  143 

way  from  what  was  expected.  All  that  Bradley  could 
prove  was  that  the  distances  of  the  stars  must  be 
hundreds  of  thousands  of  times  that  of  the  sun. 

An  introductory  remark  on  the  use  of  the  word 
parallax  may  preface  a  statement  of  the  results  of  re- 
searches now  to  be  considered. 

In  a  general  way,  the  change  of  apparent  direction 
of  an  object  arising  from  a  change  in  the  position  of 
an  observer  is  termed  parallax.  More  especially,  the 
parallax  of  a  star  is  the  difference  of  its  direction  as 
seen  from  the  sun  and  from  that  point  of  the  earth's 
orbit  from  which  the  apparent  direction  will  be 
changed  by  the  greatest  amount.  It  is  equal  to  the 
angle  subtended  by  the  radius  of  the  earth's  orbit,  as 
seen  from  the  star.  The  simplest  conception  of  an  arc 
of  one  second  is  reached  by  thinking  of  it  as  the  angle 
subtended  by  a  short  line  at  a  distance  of  206,265 
times  its  length.  To  say  that  a  star  has  a  parallax  of 
i"  would  therefore  be  the  same  thing  as  saying  that  it 
was  at  a  distance  of  206,265  times  that  of  the  earth 
from  the  sun.  A  parallax  of  one-half  a  second  implies 
a  distance  twice  as  great ;  one  of  one-third,  three 
times  as  great.  A  parallax  of  o."2O  implies  a  distance 
of  more  than  a  million  times  that  of  our  unit  of 
measure. 

The  first  conclusive  result  as  to  the  extreme  min- 
uteness of  the  parallax  of  the  brighter  stars  was 
reached  by  Struve,  at  Dorpat,  about  1830.  First  Meas- 
In  the  high  latitude  of  Dorpat  the  right  ures  of 
ascension  of  a  star  within  45°  of  the  pole  Parallax- 
can  be  determined  with  great  precision,  not  only  at 


144  THE  PARALLAXES  OF  THE  STARS 

the  moment  of  its  transit  over  the  meridian,  but  also 
at  transit  over  the  meridian  below  the  pole,  which 
occurs  twelve  hours  later.  He,  therefore,  selected  a 
large  group  of  stars  which  could  be  observed  twice 
daily  in  this  way  at  certain  times  of  the  year,  and 
made  continuous  observations  on  them  through  the 
year.  It  was  not  possible,  by  this  method,  to  cer- 
tainly detect  the  parallax  of  any  one  star.  What  was 
aimed  at  was  to  determine  the  limit  of  the  average 
parallax  of  all  the  stars  thus  observed.  The  con- 
clusion reached  was  that  this  limit  could  not  exceed 
one-tenth  of  a  second  and  that  the  average  distance 
of  the  group  could  not,  therefore,  be  much  less  than 
two  million  times  the  distance  of  the  sun.  If,  per- 
chance, some  stars  were  nearer  than  this,  others  were 
more  distant. 

By  a  singular  coincidence,  success  in  detecting  stel- 
lar parallax  was  reached  by  three  independent  inves- 
tigators almost  at  the  same  time,  observing  three 
different  stars. 

To  Bessel  is  commonly  assigned  the  credit  of  hav- 
ing first  actually  determined  the  parallax  of  a  star 
with  such  certainty  as  to  place  the  result  beyond 
question.  The  star  having  the  most  rapid  proper 
motion  on  the  celestial  sphere,  so  far  as  known  to 
Bessel,  was  61  Cygni,  which  is,  however,  only  of  the 
fifth  magnitude.  This  rapid  motion  indicated  that  it 
was  probably  among  the  stars  nearest  to  us,  much 
nearer,  in  fact,  than  the  faint  stars  by  which  it  is 
surrounded. 

After  several  futile  attempts,  he  undertook  a  series 


FIRST  MEASURES  OF  PARALLAX  145 

of  measurements,  the  best  in  his  power  to  make,  with 
a  heliometer,  in  August,  1837,  and  continued  them 
until  October,  1838.  The  object  was  to  determine, 
night  after  night,  the  position  of  61  Cygni  relative  to 
certain  small  stars  in  its  neighbourhood.  Then  he  and 
his  assistant,  Sluter,  made  a  second  series,  which  was 
continued  until  1840.  All  these  observations  showed 
conclusively  that  the  star  had  a  parallax  of  about 

o"-35- 

While  Bessel  was  making  these  observations,  Struve, 
at  Dorpat,  made  a  similar  attempt  upon  Alpha  Lyrse. 
This  star,  in  the  high  northern  latitude  of  .Dorpat, 
could  be  accurately  observed  throughout  almost  the 
entire  year.  It  is  one  of  the  brightest  stars  of  the 
northern  heavens  and  has  a  proper  motion.  There 
was,  therefore,  reason  to  believe  it  among  the  nearest  of 
the  stars.  The  observations  of  Struve  extended  from 
1835  to  August,  1838,  and  were,  therefore,  almost 
simultaneous  with  the  observations  made  by  Bessel 
on  6 1  Cygni.  He  concluded  that  the  parallax  of 
Alpha  Lyrae  was  about  one-fourth  of  a  second.  Sub- 
sequent investigations  have,  however,  made  it  proba- 
ble that  this  result  was  about  double  the  true  value  of 
the  parallax. 

The  third  successful  attempt  was  made  by  Hender- 
son, of  England,  astronomer  at  the  Cape  of  Good 
Hope.  He  found  from  meridian  observations  that 
the  star  Alpha  Centauri  had  a  parallax  of  about  i". 
This  is  a  double  star  of  the  first  magnitude  which, 
being  only  30°  from  the  south  celestial  pole,  never 
rises  in  our  latitudes.  Its  nearness  to  us  was  indicated 


i46  THE  PARALLAXES  OF  THE  STARS 

not  only  by  its  magnitude,  but  also  by  its  con- 
siderable proper  motion.  Although  subsequent  in- 
vestigation has  shown  the  parallax  of  this  body  to 
be  less  than  that  found  by  Henderson,  it  is,  up  to 
the  time  of  writing,  the  nearest  star  whose  distance 
has  been  ascertained. 

The  great  difficulty  of  detecting  an  annual  change 
in  the  direction  of  a  star  amounting  to  only  a  fraction 
of  a  second  will  be  obvious  to  the  reader.  He  will 
be  still  more  impressed  with  it  if,  looking  through  a 
powerful  telescope  at  any  star,  he  sees  how  it  flickers 
in  consequence  of  the  continual  motions  going  on  in 
the  air  through  which  it  is  seen,  and  considers  how 
difficult  it  must  be  to  fix  any  point  of  reference  from 
which  to  measure  the  change  of  direction. 

The  latter  is  the  capital  difficulty  in  measuring  the 
parallax.  How  shall  we  know  that  a  star  has  changed 
its  direction  by  a  fraction  of  a  second  in  the  course  of 
six  months  ?  There  must  be  for  this  purpose  some 
standard  direction  from  which  we  can  measure. 

The  most  certain  of  these  standard  directions  is 
that  of  the  earth's  axis  of  rotation.  It  is  true  that 
this  direction  varies  in  the  course  of  the  year,  but  the 
amount  of  the  variation  is  known  with  great  precision, 
so  that  it  can  be  properly  allowed  for  in  the  reduction 
of  the  observations.  The  angle  between  the  direc- 
tion of  a  star  and  that  of  the  earth's  axis,  the  latter 
direction  being  represented  by  the  celestial  pole,  can 
be  measured  with  our  meridian  instruments.  It  is,  in 
fact,  the  north  polar  distance  of  the  star,  or  the  com- 
plement of  its  declination.  If,  therefore,  the  astrono- 


MODERN  METHODS  147 

mer  could  measure  the  declination  of  a  star  with 
great  precision  throughout  the  entire  year,  he  would 
be  able  to  determine  its  parallax  by  a  comparison  of 
the  measures.  But  it  is  found  impossible  in  practice 
to  make  measures  of  so  long  an  arc  with  the  neces- 
sary precision.  The  uncertain  and  changing  effect  of 
the  varying  seasons  and  different  temperatures  of  day 
and  night  upon  the  air  and  the  instrument  quite  masks 
the  parallax  in  all  ordinary  cases.  After  several  at- 
tempts with  the  finest  instruments,  handled  with  the 
utmost  skill,  to  determine  stellar  parallax  from  the  de- 
clinations of  the  stars,  the  method  has  been  practically 
abandoned. 

The  method  now  practised  is  that  of  relative  paral- 
lax. By  this  method  the  standard  direction  is  that 
of  a  small  star  apparently  alongside  one  Modem 
whose  parallax  is  to  be  measured,  but,  pre-  Methods, 
sumably,  so  much  farther  away  that  it  may  be  regarded 
as  having  no  parallax.  In  this  assumption  lies  the 
weak  point  of  the  method.  Can  we  be  sure  that  the 
smaller  stars  are  really  without  appreciable  parallax  ? 
The  latest  researches  make  it  probable  that  we  can. 
It  is  now  considered  quite  safe  to  assume  that  the 
small  stars  without  proper  motion  are  so  far  away  that 
their  parallax  is  insensible. 

Until  recent  times  it  was  generally  supposed  that 
the  magnitude  of  the  stars  afforded  the  best  index  to 
their  relative  distances.  If  the  stars  were  of  the 
same  intrinsic  brilliancy,  the  amount  of  light  received 
from  them  would,  as  already  pointed  out,  have  been 
inversely  as  the  square  of  the  distance.  Although 


148  THE  PARALLAXES  OF  THE  STARS 

there  was  no  reason  to  suppose  that  any  such  equality 
really  existed,  it  would  still  remain  true  that,  in  the  gen- 
eral average,  the  brighter  stars  must  be  nearer  to 
us  than  the  fainter  ones.  But  when  the  proper 
motions  of  stars  came  to  be  investigated,  it  was  found 
that  the  amount  of  this  motion  afforded  a  better  index 
to  the  distance  than  the  magnitude  did.  The  diversity 
of  actual  or  linear  motion  is  not  so  wide  as  that  of 
absolute  brilliancy.  Stars  have,  therefore,  in  recent 
times,  been  selected  for  parallax  very  largely  on  ac- 
count of  their  proper  motion,  without  respect  to  their 
brightness. 

Ever  since  the  time  of  Bessel  the  experience  of 
practical  astronomers  has  tended  toward  the  conclu- 
sion that  the  best  instrument  for  delicate  measure- 
ments like  these  is  the  heliometer.  This  is  an 
equatorial  telescope  of  which  the  object-glass  is 
divided  along  a  diameter  into  two  semicircles,  which 
can  slide  along  each  other.  Each  half  of  the  object- 
glass  forms  a  separate  image  of  any  star  at  which  the 
telescope  may  be  pointed.  By  sliding  the  two  halves 
along  each  other,  the  images  can  be  brought  together 
or  separated  to  any  extent.  If  there  are  two  stars  in 
proximity,  the  image  of  one  star  made  by  one-half  of 
the  glass  can  be  brought  into  coincidence  with  that 
of  the  other  star  made  by  the  other  half.  The  sliding  of 
the  two  halves  to  bring  about  this  coincidence  affords 
a  scale  of  measurement  for  the  angular  distance  of  the 
two  stars. 

The  most  noteworthy  forward  steps  in  improving 
the  heliometer  are  due  to  the  celebrated  instrument- 


MODERN  METHODS  149 

makers  of  Hamburg,  the  Messrs.  Repsold,  aided  by 
the  suggestions  of  Dr.  David  Gill,  astronomer  at  the 
Cape  of  Good  Hope.  The  latter,  in  connection  with 
his  coadjutor,  Elkin,  made  an  equally  important  step 
in  the  art  of  managing  the  instrument  and  hence  in  de- 
terming  the  parallax  of  stars.  The  best  results  yet  at- 
tained are  those  of  these  two  observers,  and  of  Peter, 
of  Germany. 

Yet  more  recently,  Kapteyn,  of  Holland,  has  ap- 
plied what  has  seemed  to  be  the  unpromising  method 
of  differences  of  right  ascension  observed  with  a 
meridian  circle.  This  method  has  also  been  applied 
by  Flint,  at  Madison,  Wis.  Through  the  skill  of  these 
observers,  as  well  as  that  of  Briinnow  and  Ball,  in  ap- 
plying the  equatorial  telescope  to  the  same  purposes, 
the  parallaxes  of  nearly  one  hundred  stars  have  been 
measured  with  greater  or  less  precision. 

A  rival  method  to  that  of  the  heliometer  has  been 
discovered  in  the  photographic  telescope.  The  plan 
of  this  instrument,  and  its  application  to  such  pur- 
poses as  this,  are  extremely  simple.  We  point  a  tele- 
scope at  a  star  and  set  the  clock-work  going,  so  that  the 
telescope  shall  remain  pointed  as  exactly  as  possible  in 
the  direction  of  the  star.  We  place  a  sensitised  plate 
in  the  focus  and  leave  it  long  enough  to  form  an 
image  both  of  the  particular  star  in  view  and  of  all  the 
stars  around  it.  The  plate  being  developed,  we  have 
a  permanent  record  of  the  relative  positions  of  the 
stars  which  can  be  measured  with  a  suitable  instru- 
ment at  the  observer's  leisure.  The  ad  vantage  of  the 
method  consists  in  the  great  number  of  stars  which 


150  THE  PARALLAXES  OF  THE  STARS 

may  be  examined  for  parallax,  and  in  the  rapidity  with 
which  the  work  can  be  done. 

The  earliest  photographs  which  have  been  utilised 
in  this  way  are  those  made  by  Rutherfurd  in  New 
York  during  the  years  1860  to  1875.  The  plates  taken 
by  him  have  been  measured  and  discussed  principally 
by  Rees  and  Jacoby,  of  Columbia  University.  Before 
their  work  was  done,  however,  Pritchard,  of  Oxford, 
applied  the  method  and  published  results  in  the  case 
of  a  number  of  stars. 

One  of  the  pressing  wants  of  astronomy  at  the 
present  time  is  a  parallactic  survey  of  the  heavens  for 
the  purpose  of  discovering  all  the  stars  whose  parallax 
exceeds  some  definable  limit,  sayo".  i.  Such  a  survey 
is  possible  by  photography,  and  by  that  only.  A 
commencement,  which  may  serve  as  an  example  of  one 
way  of  conducting  the  survey,  has  been  made  by 
Kapteyn  on  photographic  negatives  taken  by  Donner 
at  Helsingfors. 

These  plates  cover  a  square  in  the  Milky  Way 
about  two  degrees  on  the  side,  extending  from  34° 
50'  in  declination  to  36°  50',  and  from  2oh.  im.  in  R. 
A.  to  2oh.  lorn.  245.  Three  plates  were  used,  on 
each  of  which  the  image  of  each  star  is  formed  twelve 
times.  Three  of  the  twelve  impressions  were  made  at 
the  epoch  of  maximum  parallactic  displacement,  six  at 
the  minimum  six  months  later,  and  three  at  the  fol- 
lowing maximum.  The  parallaxes  found  on  the  plates 
can  only  be  relative  to  the  general  mean  of  all  the 
other  stars,  and  must  therefore  be  negative  as  often  as 
positive.  The  following  positive  parallaxes,  amount- 


MODERN  METHODS  151 

ing  to  o".i,  came  out  with  some  consistency  from  the 
measures : 

Star,  B.  D.,  3972  Mag.  8.6  R.  A.  2oh.  2m.    os.  Dec.  +35°.$  Par.-fo".n 

Star,  B.  D.,  3883  Mag.  7.1  R.  A.  2oh.  2m.    35.  Dec.  +36°. i  Par.-j-o".i8 

Star,  B.  D.,4003  Mag.  9.2  R.  A.  2oh.  4m.  585.  Dec.  +35°.4  Par.-fo".ro 

Star,  B.  D.,3959  Mag.  7.0  R.  A.  2oh.  gm.  145.  Dec.  +36°. 3  Par.--(-o".io 

Against  these  are  to  be  set  negative  parallaxes  of 
— o".O9,— o".o8,  and  several  a  little  smaller,  which  are 
certainly  unreal, 

The  presumption  in  favour  of  the  actuality  of  one  or 
more  of  the  above  positive  values,  which  is  created  by 
their  excess  over  the  negative  values,  is  offset  by  the 
following  considerations  :  The  area  of  the  entire  sky 
is  more  than  40,000  square  degrees,  or  10,000  times 
the  area  covered  by  the  Helsingfors  plates.  We  can- 
not well  suppose  that  there  are  1000  stars  in  the  sky 
with  a  parallax  of  o".  10  or  more  without  violating  all 
the  probabilities  of  the  case.  The  probabilities  are 
therefore  against  even  one  star  with  such  a  parallax 
being  found  on  those  plates.  Yet  the  cases  of  these 
four  stars  are  worthy  of  further  examination,  if  any  of 
them  are  found  to  have  a  sensible  proper  motion. 

On  an  entirely  different  plan  is  a  survey  recently 
concluded  by  Chase  with  the  Yale  heliometer.  It  in- 
cludes such  stars  having  an  annual  proper  motion  of 
o".O5  or  more  as  had  not  already  been  measured  for 
parallax.  The  results,  in  statistical  form,  are  these  : 

2  stars  have  parallaxes  between  +  o".2o  and  -f-  o".25. 

6  stars  have  parallaxes  between  -j-  o'  .15  and  -f-  o".2O. 
ii  stars  have  parallaxes  between  -j-  o".io  and  -f-  o".  15. 
24  stars  have  parallaxes  between  -j-  ©".05  and  -j-  o".io. 
34  stars  have  parallaxes  between  o".oo  and  +  o".o5. 


152  THE  PARALLAXES  OF  THE  STARS 

8  stars  have  parallaxes  between  —  o".o5  and  o".oo. 
5  stars  have  parallaxes  between  —  o".io  and  —  o".o5. 
2  stars  have  parallaxes  between  —  o".i5  and  —  o".io. 

92,  total  number  of  stars. 

It  will  be  understood  that  the  negative  parallaxes 
found  for  fifteen  of  these  stars  are  the  result  of  errors 
of  observation.  Assuming  that  an  equal  number  of 
the  smaller  positive  values  are  due  to  the  same  cause, 
and  substracting  these  thirty  stars  from  the  total 
number,  we  shall  have  sixty-two  stars  left  of  which  the 
parallax  is  real  and  generally  amounts  to  o".o5  more 
or  less.  The  two  values  approximating  to  o".25  seem 
open  to  little  doubt.  We  might  say  the  same  of  the 
six  next  in  the  list.  The  first  two  belong  to  the  stars 
54  Piscium  and  Weisse,  lyh.,  322. 

A  table  of  all  the  well-determined  parallaxes  of 
stars  which  the  author  has  been  able  to  find  in  astro- 
nomical literature  will  be  found  in  the  Appendix  to 
the  present  work. 


CHAPTER  X 


SYSTEMS  OF  STARS 


and  other  suns  perhaps, 


With  their  attendant  moons  thou  wilt  descry, 

Communicating  male  and  female  light, 

Which  two  great  sexes  animate  the  world. — MlLTON. 

SIR  WILLIAM  HERSCHEL  was  the  first  to 
notice  that  many  stars  which,  to  the  unaided 
vision,  seemed  single,  were  really  composed  of  two 
stars  in  close  proximity  to  each  other.  The  first  quest- 
ion to  arise  in  such  a  case  would  be  whether  the 
proximity  is  real  or  whether  it  is  only  apparent,  arising 
from  the  two  stars  being  in  the  same  line  from  our 
system.  This  question  was  speedily  settled  by  more 
than  one  consideration.  If  there  were  no  real  con- 
nection between  any  two  stars,  the  chances  would  be 
very  much  against  their  lying  so  nearly  in  the  same 
line  from  us  as  they  are  seen  to  do  in  the  case  of  double 
stars.  Out  of  five  thousand  stars  scattered  at  random 
over  the  celestial  vault  the  chances  would  be 
against  more  than  three  or  four  being  so  close 
together  that  the  naked  eye  could  not  separate  them, 
and  would  be  hundreds  to  one  against  any  two  being 
as  close  as  the  components  of  the  closer  double  stars 
153 


i54  SYSTEMS  OF  STARS 

revealed  by  the  telescope.  The  conclusion  that  the 
proximity  is  in  nearly  all  cases  real  is  also  proved  by 
the  two  stars  of  a  pair  moving  together  or  revolving 
round  each  other. 

Altogether  there  is  no  doubt  that  in  the  case  of  the 
brighter  stars  all  that  seem  double  in  the  telescope  are 
really  companions.  But  when  we  come  to  the  thou- 
sands or  millions  of  telescopic  stars,  there  may  be  some 
cases  in  which  the  two  stars  of  a  pair  have  no  real 
connection  and  are  really  at  very  different  distances 
from  us.  The  stars  of  such  a  pair  are  called  "  opti- 
cally double."  They  have  no  especial  interest  for  us 
and  need  not  be  further  considered  in  the  present  work. 

After  Herschel,  the  first  astronomer  to  search  for 
double  stars  on  a  large  scale  was  Wilhelm  Struve,  the 
celebrated  astronomer  of  Dorpat.  So  thorough  was 
his  work  in  this  field  that  he  may  fairly  be  regarded  as 
the  founder  of  a  new  branch  of  astronomy.  Armed 
with  what  was,  at  that  time  (1815-35),  a  remarkable 
refracting  telescope,  he  made  a  careful  search  of  that 
part  of  the  sky  visible  at  Dorpat,  with  a  view  of  dis- 
covering all  the  double  stars  within  reach  of  his  instru- 
ment. The  angular  distance  apart  of  the  components 
and  the  direction  of  the  fainter  from  the  brighter  star 
were  repeatedly  measured  with  all  attainable  precision. 
The  fine  folio  volume,  Mensurte  Micrometricce,  in 
which  his  results  were  published  and  discussed,  must 
long  hold  its  place  as  a  standard  work  of  reference  on 
the  subject. 

Struve  had  a  host  of  worthy  successors,  of  whom  we 
can  name  only  a  few.  Sir  John  Herschel  was  rather 


DOUBLE  STARS 


155 


a  contemporary  than  a  successor.  His  most  notable 
work  on  double  stars  was  done  during  his  expedition 
to  the  Cape  of  Good  Hope,  where  he  discovered  a 
great  number  of  these  objects  in  the  southern  heav- 
ens with  the  great  telescope  at  his  command.  Her- 
schel,  South,  and  Dawes,  of  England,  were  amo^ng 
the  greatest  English  observers  about  the  middle  of  the 
century.  Otto  Struve,  son  of  Wilhelm,  continued  his 
father's  work  with  zeal  and  success  at  Pulkowa.  Later 
one  of  the  most  industrious  observers  was  Dembowski, 
of  Italy.  During  the  last  thirty  years  one  of  the  most 
successful  cultivators  of  double-star  astronomy  has 
been  Burnham,  of  Chicago.  He  is  to-day  the  leading 
authority  on  the  subject.  Enthusiasm,  untiring  in- 
dustry, and  wonderful  keenness  of  vision  have  com- 
bined to  secure  him  this  position. 

Let  P  be  the  principal  star  and  C  the  companion. 
Let  N  S  be  a  north  and  south 
line  through  P,  or  an  arc  of  the 
celestial  meridian,  the  direction 
N  being  north  and  S  south  from 
the  star  P. 

Then,  the  angle  N  P  C  is  called 
the  position-angle  of  the  pair.  It 
is  counted  round  the  circle  from 
o°  to  360°.  The  angle  drawn  in 
the  figure  is  nearly  120°.  Were 
the  companion  C  in  the  direction 
S  the  position-angle  would  be  180°;  to  the  right  of 
P  it  would  be  270°;  to  the  right  of  N  it  would  be 
between  270°  and  360°. 


156  SYSTEMS  OF  STARS 

The  distance  is  the  angle  P  C  between  the  compon- 
ents which  is  expressed  in  seconds  of  arc. 

The  following  definitions  and  explanations  will  be 
useful  to  the  general  reader.  The  two  stars  of  a  pair 
are  called  its  components.  The  lesser  is  called  the 
companion  of  the  brighter.  To  separate  a  pair  means 
to  distinguish  the  two  stars  of  the  pair.  The  particu- 
lars which  the  careful  observer  of  a  double  star  should 
record  are  the  position-angle  and  distance  of  the  com- 
ponents and  their  respective  magnitudes.  To  these 
Struve  added  their  colours  ;  but  *f  his  has  not  gen- 
erally been  done. 

We  cannot  set  any  well-defined  limit  to  the  range 
of  distance.  The  general  rule  is  that  the  greater  the 
distance  beyond  a  few  seconds  the  less  the  interest 
that  attaches  to  a  double  star,  partly  because  the  ob- 
servation of  distant  pairs  offers  no  difficulty,  partly 
because  of  the  increasing  possibility  that  the  compon- 
ents have  no  physical  connection,  and  so  form  only 
an  optically  double  star.  With  every  increase  of 
telescopic  power  so  many  closer  and  closer  pairs  are 
found  that  we  cannot  set  any  limit  to  the  number  of 
stars  that  may  have  companions.  It  is  therefore  to 
the  closer  pairs  that  the  attention  of  astronomers  is 
more  especially  directed. 

The  difficulty  of  seeing  a  star  as  double,  or,  in  the 
familiar  language  of  observers,  of  "  separating "  the 
components,  arises  from  two  sources,  the  proximity  of 
the  companion  to  the  principal  star,  and  the  difference 
in  magnitude  between  the  two.  It  was  only  in  rare 
cases  that  Struve  could  separate  a  pair  as  close  as 


BINARY  SYSTEMS  157 

half  a  second.  Now  Burnham  finds  pairs  whose  dis- 
tance is  less  than  one-quarter  of  a  second  ;  indeed  the 
limit  of  a  tenth  of  a  second  is  being  approached.  It 
goes  without  saying  that  a  very  minute  companion  to 
a  bright  star  may,  when  the  distance  is  small,  be  lost 
in  the  rays  of  its  brighter  neighbour.  For  all  these 
reasons  no  estimate  can  be  made  of  the  actual  number 
of  double  stars  in  the  heavens.  With  every  increase 
of  telescopic  power  and  observing  skill  more  difficult 
pairs  are  being  found,  without  any  indication  of  a 
limit. 

The  great  interest  which  attaches  to  double  stars 
arises  from  the  proof  which  they  afford  that  the  law 
of  gravitation  extends  to  the  stars.  Struve,  by  com- 
paring his  own  observations  with  each  other,  or  with 
those  of  Herschel,  found  that  many  of  the  pairs 
which  he  measured  were  in  relative  motion  ;  the  posi- 
tion-angle progressively  changing  from  year  to  year, 
and  sometimes  the  distance  also.  The  lesser  star  was 
therefore  revolving  round  the  greater,  or,  to  speak 
with  more  precision,  both  were  revolving  round  their 
common  centre  of  gravity.  To  such  a  pair  the  name 
binary  system  is  now  applied. 

There  can  be  no  reasonable  doubt  that  the  two 
components  of  all  physically  connected  double  stars 
revolve  round  each  other.  If  they  did  not  their 
mutual  gravitation  would  bring  them  together  and 
fuse  them  into  a  single  mass.  We  are  therefore  justi- 
fied in  considering  all  double  stars  as  binary  systems, 
except  those  which  are  merely  optically  double.  For 
reasons  already  set  forth,  the  pairs  of  the  latter  class 


158  SYSTEMS  OF  STARS 

which  are  near  together  must  be  very  few  in  number ; 
indeed,  there  are  probably  none  among  the  close 
double  stars  whose  brightest  component  can  be  seen 
optically  by  the  naked  eye. 

The  time  of  revolution  of  the  binary  systems  is  so 
long  that  there  are  only  about  fifty  cases  in  which  it 
has  yet  been  determined  with  any  certainty.  Leav- 
ing out  the  "  spectroscopic  binaries,"  to  be  hereafter 
described,  the  shortest  period  yet  fully  established 
is  eleven  years.  In  only  a  small  minority  of  cases 
is  the  period  less  than  a  century.  In  the  large 
majority  either  no  motion  at  all  has  yet  been  de- 
tected, or  it  is  so  slow  as  to  indicate  that  the  period 
must  be  several  centuries,  perhaps  several  thousand 
years. 

There  is  great  difficulty  in  determining  the  period, 
with  precision  until  the  stars  have  been  observed 
through  nearly  a  revolution,  owing  to  the  number  of 
elements,  seven  in  all,  that  fix  the  orbit,  and  the  diffi- 
culty of  making  the  measures  of  position-angle  and 
distance  with  precision.  It  thus  happens  that  many 
of  the  orbits  of  binary  systems  which  have  been  com- 
puted and  published  have  no  sound  basis.  Two  cases 
in  point  may  be  mentioned. 

The  first-magnitude  star  Castor  or  Alpha  Gemino- 
rum  is  seen  to  be  double  with  quite  a  small  telescope. 
The  components  are  in  relative  motion.  Owing  to  the 
interesting  character  of  the  pair  it  has  been  well  ob- 
served, and  a  number  of  orbits  have  been  computed. 
The  periodic  times  found  by  the  computers  have  a 
wide  range.  The  fact  is,  nothing  is  known  of  the 


BINARY  SYSTEMS  159 

period  except  that  it  is  to  be  measured  by  centuries, 
perhaps  by  thousands  of  years. 

The  history  of  61  Cygni,  a  star  ever  memorable 
from  being  the  first  of  which  the  parallax  was  determ- 
mined,  is  quite  similar.  Although,  since  accurate  ob- 
servations have  been  made  on  it,  the  components 
have  moved  through  an  apparent  angle  of  30°,  the  ob- 
servations barely  suffice  to  show  a  very  slight  curva- 
ture in  the  path  which  the  two  bodies  are  describing 
round  each  other.  Whether  the  period  is  to  be 
measured  by  centuries  or  by  thousands  of  years  can- 
not be  determined  for  many  years  to  come. 

In  his  work  on  the  Evolution  of  the  Stellar  Systems, 
Prof.  T.  J.  J.  See  has  investigated  the  orbits  of  forty 
double  stars  having  the  shortest  periods.  There  are 
twenty-eight  periods  of  less  than  one  hundred  years. 

In  considering  the  orbits  of  binary  systems  we  must 
distinguish  between  the  actual  and  the  apparent  orbit. 
The  former  is  the  orbit  as  it  would  appear  to  an  ob- 
server looking  at  it  from  a  direction  perpendicular  to 
its  plane.  This  orbit,  like  that  of  a  planet  or  comet 
moving  round  the  sun,  is  an  ellipse,  having  the  princi- 
pal star  in  its  focus.  The  point  nearest  the  latter  is 
called  the  periastron,  or  pericentre,  and  corresponds 
to  the  perihelion  of  a  planetary  orbit.  The  point 
most  distant  from  the  principal  star  is  the  apocentre. 
It  is  opposite  the  pericentre  and  corresponds  to  the 
aphelion  of  a  planetary  orbit.  The  law  of  motion  is 
here  the  same  as  in  the  case  of  a  body  of  the  solar  sys- 
tem ;  the  radius  vector  joining  the  two  bodies  sweeps 
over  equal  areas  in  equal  times. 


i6o  SYSTEMS  OF  STARS 

The  apparent  orbit  is  the  orbit  as  it  appears  to  us. 
It  differs  from  the  actual  orbit  because  we  see  it  from 
a  more  or  less  oblique  direction.  In  some  cases  the 
plane  of  the  orbit  passes  near  our  system.  Then  to 
us  the  orbit  will  appear  as  a  straight  line  and  the 
small  star  will  seem  to  swing  from  one  side  of  the 
large  one  to  the  other  like  a  pendulum,  though  the  ac- 
tual orbit  may  differ  little  from  a  circle.  In  some 
cases  there  may  be  two  pei  icentres  and  two  apocentres 
to  the  apparent  orbit.  This  will  be  the  case  when  a 
nearly  circular  orbit  is  seen  at  a  considerable 
obliquity. 

It  is  a  remarkable  and  interesting  fact  that  the  law 
of  areas  holds  good  in  the  apparent  as  in  the  actual 
orbit.  This  is  because  all  parts  of  the  plane  of  the 
orbit  are  seen  at  the  same  angle,  so  that  the  obliquity 
of  vision  diminishes  all  the  equal  areas  in  the  same 
proportion  and  thus  leaves  them  equal. 

The  two  most  interesting  binary  systems  are  those 
of  Sirius  and  Procyon.     In  the  case  of  each  the  exist- 
ence and  orbit  of  the  companion  were  in- 
Binary 

Systems  of  ferred  from  the  motions  of  the  principal 
Sirius  and  star  before  the  companion  had  been  seen. 
Before  the  middle  of  the  century  it  was 
found  that  Sirius  did  not  move  with  the  uniform 
proper  motion  which  characterises  the  stars  in  general ; 
and  the  inequality  of  its  motion  was  attributed  to  the 
attraction  of  an  unseen  satellite.  Later  Auwers,  from 
an  exhaustive  investigation  of  all  the  observations  of 
the  star,  placed  the  inequality  beyond  doubt  and 
determined  the  elements  of  the  orbit  of  the  otherwise 


SIR  I  US  AND  P ROC  YON  161 

unknown  satellite.  Before  his  final  work  was  pub- 
lished the  satellite  was  discovered  by  Alvan  G.  Clark, 
of  Cambridgeport,  Mass.,  son  and  successor  of  the 
first  and  greatest  American  maker  of  telescopes.  Ad- 
ditional interest  was  imparted  to  the  discovery  by  the 
fact  that  it  was  made  in  testing  a  newly  constructed 
telescope,  the  largest  refractor  that  had  been  made  up 
to  that  time.  The  discoverer  was,  at  the  time,  un- 
aware of  the  work  of  Peters  and  Auwers  demonstrat- 
ing the  existence  of  the  satellite.  The  latter  was, 
however,  in  the  direction  predicted  by  Auwers,  and  a 
few  years  of  observation  showed  that  it  was  moving  in 
fairly  close  accordance  with  the  prediction. 

The  orbit  as  seen  from  the  earth  is  very  eccentric, 
the  greatest  distance  of  the  satellite  from  the  star 
being  about  ten  seconds,  the  least  less  than  three 
seconds.  Owing  to  the  brilliant  light  of  Sirius  the 
satellite  is  quite  invisible,  even  in  the  most  powerful 
telescopes,  when  nearest  its  primary.  This  was  the 
case  in  the  years  1890-92  and  will  again  be  the  case 
about  1940,  when  another  revolution  will  be  completed. 

The  history  of  Procyon  is  remarkably  similar.  An 
inequality  of  its  motion  was  suspected  by  Peters,  but 
not  proved.  Auwers  showed  from  observations  that 
it  described  an  orbit  seemingly  circular,  having  a  radius 
of  about  i".  There  could  be  no  doubt  that  this 
motion  must  be  due  to  the  revolution  of  a  satellite,  but 
the  latter  long  evaded  discovery,  though  carefully 
searched  for  with  the  new  telescopes  which  were  from 
time  to  time  brought  into  use.  At  length  in  1895 
Schaeberle  found  the  long-looked-for  object  with  the 


162 


SYSTEMS  OF  STARS 


36-inch  telescope  of  the  Lick  Observatory.  It  was 
nearly  in  the  direction  predicted  by  Auwers,  and  a 
year's  observation  by  Schaeberle,  Barnard,  and  others 
showed  that  it  was  revolving  in  accordance  with  the 
theory. 

If  the  conclusion  of  Auwers  that  the  apparent  orbit 
of  the  principal  star  is  circular  were  correct,  the  distance 
of  the  satellite  should  always  be  the  same.  It  would 

then  be  equally  easy  to 
see  at  all  times.  The  fact 
that  neither  Burnham  nor 
Barnard  had  previously 
been  able  to  see  the  object 
with  the  Lick  telescope 
would  then  be  difficult  to 
account  for.  The  fact  is, 
however,  that  the  periodic 
motion  of  Procyon  is  so 
small  that  a  considerable 
eccentricity  might  exist 
without  being  detected  by 
observations.  The  prob- 

Fi&.2.  *i\       \       ability   is,  therefore,   that 

the  apparent  orbit  is 
markedly  eccentric  and 
that  the  satellite  was 
nearer  the  primary  during  the  years  1878-92  than  it 
was  when  discovered. 

One  very  curious  feature,  common  to  both  of  these 
systems,  is  that  the  mass  of  each  satellite,  as  compared 
with  that  of  its  primary,  is  out  of  all  proportion  to  its 


APPARENT  ORBIT  OF  «  CENTAURI,  BY 
PROFESSOR   SEE 


TRIPLE  AND  MULTIPLE  SYSTEMS 


163 


brightness.  The  remarkable  conclusions  to  be  drawn 
from  this  fact  will  be  discussed  in  a  subsequent  chapter. 

The  system  of  Alpha  Centauri  is  interesting  from  the 
shortness  of  the  period,  the  brightness  of  the  stars,  and 
the  fact  that  it  is  the  nearest  star  to  us,  so  far  as 
known.  We  reproduce  a  diagram  of  the  apparent 
orbit  from  Dr.  See's  work.  The  period  of  revolution 
found  by  Dr.  See  is  eighty-one  years.  The  major 
axis  of  the  apparent  orbit  is  32"  ;  the  minor  axis  6". 

Special  interest  attaches  to  binary  systems  of  short 
period.  Omitting  Capella,  which  will  be  described 
later,  it  does  not  seem  that  a  well-established  period 
of  less  than  eleven  years  is  known,  though  several  are 
suspected.  Among  the  pairs  of  which  the  period  of 
revolution  is  the  shortest  are  these : 

YEARS 

Period  =11. 42 
9°37'         " 


Dec.= 


K  Pegasi  :    R.  A.  =2ih.  4om. 

$  Equulei  :     "      =2ih.  zom. 

ft  883  :  "      =  4h.  45m.       "  -f  io°52'         "      =15.80 

£  Sagittarii:  "      =i8h.  56m.      "  —  30°   i'         "      =18.85 

p  Argus  :  =   7h.  47m. 

85  Pegasi :      "      =23!!.  57m.       "  -f-  26°34'  =24.00 

Shorter  periods  than  these  have  been  suspected  in 
the  cases  of  x  Pegasi  and  ft  883.  Dr.  See  considers 
that  the  period  of  ft  883  is  only  five  and  one-half 
years,  but  the  extreme  difficulty  of  the  observations 
still  leaves  room  for  question. 

Systems  of  three  or  more  stars  so  close  together  that 
there  must  be  a  physical  connection  between  Triple  and 
them  are  quite  numerous.  There  is  every  Multiple 
variety  of  such  systems.  Sometimes  a  small  systems- 
companion  of  a  brighter  star  is  found  to  be  itself 


164  SYSTEMS  OF  STARS 

double.  A  curious  case  of  this  sort  is  that  of  Gamma 
Andromedae.  This  object  was  observed  and  measured 
by  Struve  as  an  ordinary  double  star,  of  which  the  com- 
panion was  much  smaller  than  the  principal  star. 
Some  years  later  Alvan  Clark  found  that  this  com- 
panion was  itself  a  close  double  star,  of  which  the 
components,  separated  by  about  i",  were  nearly  equal. 
Moreover,  it  was  soon  found  that  these  components  re- 
volved round  each  other  in  a  period  not  yet  accurately 
determined,  but  probably  less  than  a  century.  Thus 
we  have  a  binary  system  revolving  round  a  central 
star  as  the  earth  and  moon  revolve  round  the  sun. 

In  most  triple  systems  there  is  no  such  regularity  as 
this.  The  magnitudes  and  relative  positions  of  the 
components  are  so  varied  that  no  general  description 
is  possible.  Stars  of  every  degree  of  brightness  are 
combined  in  every  way.  Observations  on  these  sys- 
tems extend  over  so  short  an  interval  that  we  have  no 
data  for  determining  the  laws  of  motion  that  may  pre- 
vail in  any  but  one  or  two  of  the  simplest  cases.  They 
are,  in  all  probability,  too  complicated  to  admit  of 
profitable  mathematical  investigation.  There  is, 
therefore,  little  more  of  interest  to  be  said  about  them. 

There  is  a  very  notable  multiple  system  known  as 
the  Trapezium  of  Orion  from  the  fact  that  it  is  com- 
posed of  four  stars.  They  are  so  close  together  as  to 
appear  like  a  single  star  to  the  naked  eye,  but  may  be 
well  separated  in  the  smallest  telescope.  There  are 
also  two  other  very  faint  stars,  each  of  which  seems  to 
be  a  companion  of  one  of  the  bright  ones.  This 
system  is  situated  in  the  great  nebula  of  Orion,  to  be 


SPECTROSCOPIC  BINAR  Y  S Y STEMS.  1 65 

described  in  the  next  chapter,  a  circumstance  which 
has  made  it  one  of  the  most  interesting  objects  to  ob- 
servers. No  motion  has  yet  been  certainly  detected 
among  the  components. 

Among  the  many  striking  results  of  recent  astro- 
nomical research  it  would  be  difficult  to  name  any 
more  epoch-making  than  the  discovery  that 

r     i  i  •       •    -i  i  Spectre- 

great  numbers  01  the  stars  have    invisible  scopic 

dark  bodies  revolving  round  them  of  a  mass  Binary  Sys- 
comparable  with  their  own.  The  existence 
of  these  revolving  bodies  is  made  known  not  only  by 
their  eclipsing  the  star,  -as  explained  in  the  chapter  on 
Variable  Stars,  but  by  their  producing  a  periodic 
change  in  the  radial  motion  of  the  star.  How  this 
motion  is  determined  by  means  of  the  spectroscope 
has  been  briefly  set  forth  in  a  former  chapter.  As  a 
general  rule  the  motion  is  uniform  in  the  case  of  each 
star.  We  have  described  in  a  former  chapter  the 
periodic  character  of  the  radial  motion  of  Algol,  dis- 
covered by  Vogel.  This  was  followed  by  the  discovery 
that  Alpha  Virginis,  though  not  variable,  was  affected 
by  a  similar  inequality  of  the  radial  motion,  having  a 
period  of  four  days  and  nineteen  minutes.  The 
velocity  of  the  star  in  its  apparent  orbit  is  very  great, 
— about  ninety-one  kilometres,  or  fifty-six  English 
miles,  per  second.  It  follows  that  the  radius  of  the 
orbit  is  some  three  million  miles.  The  mass  of  the  in- 
visible companion  must,  therefore,  be  very  great. 

A  new  form  of  binary  system  was  thus  brought  out, 
which,  from  the  method  of  discovery,  was  called  the 
spectroscopic  binary  system.  But  there  is  really  no  line 


1 66  SYSTEMS  OF  STARS 

to  be  drawn  between  these  and  other  binary  systems. 
We  have  seen  that  as  telescopic  power  is  increased, 
closer  and  closer  binary  systems  are  constantly  being 
found.  We  naturally  infer  that  there  is  no  limit  to 
the  proximity  of  the  pairs  of  stars  of  such  systems,  and 
that  innumerable  stars  may  have  satellites,  planets,  or 
companion  stars  so  close  or  so  faint  as  to  elude  our 
powers  of  observation. 

The  actual  orbit  of  such  a  system  ca'nnot  be  determ- 
ined with  the  spectroscope,  because  only  one  com- 
ponent of  the  motion,  that  in  the  direction  of  the 
earth,  can  be  observed.  In  the  case  of  an  orbit  of 
which  the  plane  was  perpendicular  to  the  line  of  sight 

.    from  the  earth  to  the 

L  MSI 

;  »  star  the  spectroscope 
I  /  could  give  us  no  infor- 
/A  mation  as  to  the  mo- 

RADIAL  MOTION  OF  A  BINARY  SYSTEM  t|on>         J}le     mOtion     tO 

or  from  the  earth  would  be  invariable.  To  show  the 
result  of  the  orbit's  being  seen  obliquely,  let  E  be  the 
earth  and  A  S  be  the  plane  of  the  orbit  seen  edgewise. 
Drop  the  perpendicular  A  M  upon  the  line  of  sight. 
Then,  while  the  star  is  moving  from  S  to  A  the  spec- 
troscope will  measure  the  motion  as  if  it  took  place 
from  S  to  M.  Since  S  M  is  less  than  A  S,  the  measured 
velocity  will  always  be  less  than  the  actual  velocity, 
except  in  the  rare  case  when  the  motion  of  the  star  is 
directed  toward  the  earth.  Since  the  spectroscope 
can  give  us  no  information  as  to  the  inclination  under 
which  we  see  the  orbit,  it  follows  that  the  actual 
orbital  velocities  of  the  spectroscopic  binaries  must 


SPECTROSCOPIC  BINAR  Y  SYSTEMS  167 

remain  unknown.  We  can  only  say  that  they  cannot 
be  less,  but  may  be  greater  to  any  extent,  than  that 
shown  by  our  measures. 

If  the  components  of  a  spectroscopic  binary  system 
do  not  differ  greatly  in  brightness,  its  character  may  be 
detected  without  actually  measuring  the  radial  veloc- 
ities. Since  the  motion  is  shown  by  a  displacement  of 
the  spectral  lines,  and  since  in  any  binary  system  the 
two  components  must  always  move  in  opposite  direc- 
tions, it  follows  that  the  displacements  of  the  spectral 
lines  of  the  two  stars  will  be  in  opposite  directions. 
Hence,  when  one  of  the  stars,  say  A,  is  moving 
towards  us,  and  the  other,  say  D,  from  us,  all  the 
spectral  lines  common  to  the  two  will  appear  double, 
the  lines  made  by  A  being  displaced  toward  the  blue 
end  of  the  spectrum  and  those  by  B  toward  the  red 
end.  After  half  a  revolution  the  motion  will  be  re- 
versed and  the  lines  will  again  be  double  ;  only  the 
lines  of  star  A  will  now  be  on  the  red  side  of  the 
others.  Between  these  two  phases  will  be  one  in 
which  the  radial  velocities  of  the  two  stars  are  the 
same  ;  the  lines  will  then  appear  single. 

The  first  star  of  which  the  binary  character  was 
detected  in  this  way  is  Xi  Ursae  Majoris.  The 
discovery  was  made  at  the  Harvard  Observatory. 

The  perfection  of  the  spectroscopic  method  is  of  so 
recent  date  that  only  binary  systems  of  comparatively 
short  period  have  so  far  been  certainly  detected. 
It  is  quite  likely  that  nearly  all  double  stars  so  bright 
that  their  spectrum  can  be  accurately  measured  for 
the  purpose  of  radial  motion  will  eventually  be 


1 68  SYSTEMS  OF  STARS 

investigated  with  the  spectroscope.  But,  so  far,  there 
has  been  no  time  to  determine  an  orbit  of  long  period 
from  the  radial  motion.  There  has  therefore  been  a 
wide  gap  between  the  shortest  period  of  a  visual 
binary  system  and  the  longest  of  a  spectroscopic 
binary. 

Quite  recently,  however,  this  gap  has  been  filled  in  a 
remarkable  way.  Early  in  1900  it  was  found  by 
Campbell,  and  independently  by  Newall,  at  Cam- 
bridge, that  Capella  was  a  spectroscopic  binary  in 
whose  spectrum  two  types  were  superimposed.  There 
was  first  the  regular  spectrum  of  the  second  type,  of- 
fering a  remarkable  resemblance  to  that  of  our  sun  ; 
superimposed  on  this  was  a  second  spectrum  similar  to 
that  of  Procyon.  Between  the  lines  of  these  two 
spectra  a  relative  motion  was  found  with  a  period  of 
104  days. 

With  the  new  28-inch  telescope  of  the  Greenwich 
Observatory  the  observers  have  been  able  to  see  the 
duplicity  of  Capella  and,  measuring  the  position-angle 
from  time  to  time,  found  a  period  substantially  the 
same  as  that  derived  from  the  radial  motions.  The 
components  were  too  close  together  to  admit  of  their 
distance  being  accurately  measured.  The  best  estim- 
ates that  could  be  made  placed  it  at  less  than  one 
tenth  of  a  second,  probably  about  o".o8.  This  is 
about  equal  to  the  parallax  of  the  star,  as  measured  by 
Elkin.  The  two  stars  did  not  seem  to  differ  much  in 
brightness.  The  conclusion  to  be  drawn  is  that  the 
actual  distance  of  the  components  is  not  very  different 
from  the  distance  between  the  earth  and  sun.  The 


STAR-  CL  USTERS  1 69 

fact  that  they  revolve  in  less  than  one-third  the  time 
that  our  earth  does  shows  that  the  combined  mass  of 
the  two  bodies  must  be  about  ten  times  that  of  the 
sun. 

It  is  very  remarkable  in  this  connection  that  the  ob- 
servations at  Greenwich  have  not,  so  far,  been  con- 
firmed at  Mount  Hamilton,  where  the  telescope  is 
more  powerful  and  the  conditions  of  seeing  supposed 
to  be  of  the  best,  nor  at  the  Yerkes  Observatory. 

A  star-cluster  is  a  bunch  or  collection  of  stars 
separated  from  the  great  mass  of  stars  which  stud  the 
heavens.  The  Pleiades,  or  "  Seven  Stars  "  star- 

as  they  are  familiarly  called,  form  a  cluster  clusters 
of  which  six  of  the  components  are  easily  seen  by  the 
naked  eye  while  five  others  may  be  distinguished  by  a 
good  eye  without  a  telescope. 

About  1780  Michell,  of  England,  raised  the  quest- 
ion whether,  supposing  the  stars  visible  to  the  naked 
eye  to  be  scattered  over  the  sky  at  random,  there 
would  be  a  reasonable  possibility  that  those  of  the 
Pleiades  would  all  fall  within  so  small  a  space  as  that 
filled  by  the  constellation.  His  correct  conclusion 
was  in  the  negative.  It  follows  that  this  cluster  does 
not  consist  of  disconnected  stars  at  various  distances, 
which  happen  to  be  nearly  in  a  line  from  our  system, 
but  is  really  a  collection  of  stars  by  itself.  Besides 
the  stars  visible  to  the  naked  eye,  the  Pleiades  com- 
prise a  great  number  of  telescopic  stars,  of  which 
about  sixty  have  been  catalogued  and  their  relative 
positions  determined.  The  principal  star  of  the  clus- 
ter is  Alcyone  or  Eta  Tauri,  which  is  of  the  third 


170  SYSTEMS  OF  STARS 

magnitude.  The  five  which  come  next  in  the  order  of 
brightness  are  not  very  unequal,  being  all  between  the 
fourth  and  fifth  magnitudes.  Six  are  near  the  sixth 
magnitude.  The  remainder,  so  far  as  catalogued, 
range  from  the  seventh  to  the  ninth. 

In  this  case  there  is  a  fairly  good  method  of  dis- 
tinguishing between  a  star  which  belongs  to  the 
cluster  and  one  which  probably  lies  beyond  it.  This 
test  is  afforded  by  the  proper  motion.  We  have 
stated  in  Chapter  VI  that  all  the  stars  of  the  group 
have  a  common  proper  motion  in  the  same  direction. 
The  amount  of  this  motion  is  about  7"  per  century. 
The  first  accurate  measures  made  on  the  relative  posi- 
tions of  the  stars  of  the  cluster  were  those  of  Bessel, 
about  1830.  In  recent  years  several  observers  have 
made  yet  more  accurate  determinations.  The  most 
thorough  recent  discussion  is  by  Elkin.  One  result 
of  his  work  is  that  there  is  as  yet  no  certain  evidence 
of  any  relative  motion  among  the  stars  of  the  group. 
They  all  move  on  together  with  their  common  motion 
of  7"  per  century,  as  if  they  were  a  single  mass. 

A  closer  cluster,  which  is  plainly  visible  to  the 
naked  eye  and  looks  like  a  cloudy  patch  of  light,  is 
Praesepe  in  the  constellation  Cancer.  It  is  very  well 
seen  in  the  early  evenings  of  winter  and  spring.  Al- 
though there  is  nothing  in  the  naked-eye  view  to 
suggest  a  star,  it  is  found  on  telescopic  examination 
that  the  individual  stars  do  not  fall  far  below  the 
limit  of  visibility,  several  being  of  about  the  seventh 
magnitude.  . 

Another  notable  cluster  of  the  same  general  nature 


STAR-CL  USTERS 


171 


is  that  in   Perseus.     This  constellation  is  situated  in 
the  Milky  Way,  not  far  from  its  region  of  nearest  ap- 


THE  GREAT  CLUSTER  IN  HERCULES,  AS  PHOTOGRAPHED  WITH  THE 
CROSSLEY  REFLECTOR  OF  THE  LICK  OBSERVATORY 

proach  to  the  pole.  In  the  figure  of  the  constellation 
the  cluster  forms  the  handle  of  the  hero's  sword.  It 
may  be  seen  in  the  evening  during  almost  any  season 


i7*2  SYSTEMS  OF  STARS. 

except  summer.  To  the  naked  eye  it  seems  more 
diffused  and  star-like  than  Praesepe  ;  in  fact,  it  has  two 
distinct  centres  of  condensation,  so  that  it  may  be  con- 
sitiered  as  a  double  cluster. 

The  two  clusters  last  described  may  be  resolved 
into  stars  with  the  smallest  telescopes.  But  in  the 
case  of  most  of  these  objects  the  individual  stars  are 
so  faint  that  the  most  powerful  instruments  scarcely 
suffice  to  bring  them  out.  One  of  the  most  remark- 
able clusters  in  the  northern  heavens  is  that  of  Her- 
cules. To  the  naked  eye  it  is  but  a  faint  and 
insignificant  patch,  which  would  be  noticed  only  by  a 
careful  observer,  but  in  a  large  telescope  it  is  seen 
to  be  one  of  the  most  interesting  objects  in  the 
heavens.  Near  the  border  the  individual  stars  can  be 
readily  distinguished,  but  they  grow  continually 
thicker  toward  the  centre,  where,  even  in  a  telescope 
of  two  feet  aperture,  the  observer  can  see  only  a 
patch  of  light,  which  is,  however,  as  he  scans  it,  sug- 
gestive of  the  countless  stars  that  must  there  be 
collected.  By  the  aid  of  photography,  Professor 
Pickering  nearly  succeeded  in  the  complete  resolution 
of  this  cluster,  and  Keeler  was  even  more  successful 
with  the  Crossley  reflector  of  the  Lick  Observatory. 

In  many  cases  the  central  portions  of  these  objects 
are  so  condensed  that  they  cannot  be  visually  resolved 
into  their  separate  stars,  even  with  the  most  power- 
ful telescopes.  A  closer  approach  to  complete  resol- 
ution has  been  made  by  photography.  We  reproduce 
photographs  of  two  noted  clusters  which  show  their 
appearance  in  a  powerful  telescope. 


STAR-CL  US  TERS.  173 

The  cluster  which,  according  to  Pickering,  may  be 
called  the  finest  in  the  sky,  is  Omega  Centauri.  It  lies 
just  within  the  border  of  the  Milky  Way,  in  right  as- 
cension i3h.  2O.8m.,  and  declination  —  46°  47'.  There 
are  no  bright  stars  near.  To  the  naked  eye  it  appears 
as  a  hazy  star  of  the  fourth  magnitude.  Its  actual  ex- 
treme diameter  is  about  40'.  The  brightest  individual 
stars  within  this  region  are  between  the  eighth  and 
ninth  magnitudes.  Over  six  thousand  have  been 
counted  on  one  of  the  photographs,  and  the  whole 
number  is  much  greater.  (See  Figure  on  page  175.) 

The  most  remarkable  and  suggestive  feature  of  the 
principal  clusters  is  the  number  of  variable  stars 
which  they  contain.  This  feature  has  been  brought 
out  by  the  photographs  taken  at  the  Harvard  Observ- 
atory and  at  its  branch  station  in  Arequipa.  The 
count  of  stars  and  the  detection  of  the  variables  was 
very  largely  made  by  Professor  Bailey,  who  for  sev- 
eral years  past  has  been  in  charge  of  the  Arequipa 
station. 

The  results  of  his  examination  of  the  photographs 
are  given  in  the  table  below.1  In  this  table,  the  first 
number  is  that  of  the  new  general  catalogue  of 
Dreyer.  The  second  column  gives  the  usual  designa- 
tion of  the  cluster,  generally  its  number  in  Messier's 
list.  The  next  two  columns  give  the  position  re- 
ferred to  the  equinox  of  1900.  Next  follows  die 
approximate  number  of  stars  examined.  The  other 
columns  are  sufficiently  explained  by  their  headings. 

1  Harvard  College  Observatory  Circular  No.  jj. 


174 


SYSTEMS  OF  STARS. 
VARIABLE  STARS  IN  CLUSTERS 


DESIGNATION. 

POSITION  1900 

R.  A.                          DEC. 

NO  STARS 
EX- 

AREA 
HX- 

NO. 

OF 

PROPORTION. 

h.   m.        °      ' 

sq.min. 

7 

FRACT. 

I    IN. 

104  47  Tucanae 

o  19.6  —  72  38 

2OOO 

1257         6 

.003 

333 

362 

o  58.9  —71  23 

675 

3H       U 

.021 

48 

(86g 

}  884 

2    12.0   -(-56   41   ) 

2  15.4  +56  39  f 

IO5O 

10800 

I 

.001 

1050 

1904  Messier  79 

5  20.i   —24  37 

2OO 

79 

5 

.025 

40 

3293 

10  29.6  —57  40 

724 

3'4 

0 

000 



4755  *  Crucis 

12  47.7  —59  48 

555 

314        o    .000 



5139  c<o  Centauri 

13  20.8  —46  47 

3000 

1257    125    .042 

24 

5272  Messier  3 

13  37.6  +28  53 

900 

1257     132     .147 

7 

5904  Messier  5 

15   13-5  +  2  27 

900       1257       85     .094 

n 

5986 

15  39-5  —37  26 

289         314         i 

.003 

289 

6093  Messier  So 

16  i  i.  i  —  22  44 

145           79 

2 

.014 

72 

6205  Messier  13 

16  38.1  +36  39 

looo         177 

2 

.002 

500 

6266  Messier  62 

16  54.9  —29  58 

960 

2l8  |     26     .027 

37 

6397 

17  32.5  —53  37 

487 

218            2       .004 

244 

6626  Messier  28 

18  18.4  —24  55 

900 

314 

9     .010 

IOO 

6656  Messier  22 

18  30.3  —23  59 

1550 

218 

16     .010 

97 

6723 

18  52.8  —36  46 

900 

314 

16    .018 

56 

6752 

19     2.0  —  60     8 

600 

218 

1       .002 

600 

6809  Messier  55 

19  33-7  —3i   10 

440 

218 

2  !   .005 

220 

7078  Messier  15 

21  25.2  +11  44 

900 

1257 

51 

.057 

IS 

7089  Messier  2 

21  28.3  —  i   16 

600 

218 

10 

.017 

60 

7099  Messier  30 

21    34.7    —23    38 

275 

218 

3 

.Oil 

92 

19050 

20380 

509 

It  will  be  seen  from  this  table  that  the  pro- 
portion of  variables  is  very  different  in  different  clus- 
ters. In  the  double  cluster  869-884,  only  one  has 
been  found  among  a  thousand  stars.  The  richest  in 
variables  is  Messier  3,  in  which  one  variable  has 
been  detected  among  every  seven  stars.  It  might  be 
suspected  that  the  closer  and  more  condensed  the 
cluster  the  greater  the  proportion  of  variables.  This, 
however,  does  not  hold  universally  true.  In  the 
great  cluster  of  Hercules  only  two  variables  are 
found  amonof  a  thousand  stars. 


STAR-CLUSTERS. 


Very  remarkable,  at  least  in  the  case  of  Omega 
Centauri,  is  the  shortness  of  the  period  of  the  variables. 
Out  of  125  found,  98  have  periods  less  than  twenty- 


THE  CLUSTER  ">  CENTAURI,  PHOTOGRAPHED  BY  GILL  AT  THE  CAPE  OBSERVATORY. 

four  hours.     On  the  subject   of  the  law  of  variation 
in  these  cases,  Pickering  says  : 

"The  light  curves  of  the  ninety-eight  stars  whose  periods  are 
less  than  twenty-four  hours  may  be  divided  into  four  classes.  The 
first  is  well  represented  by  No.  74.  The  period  of  this  star  is 
i2h.  401.  3.  and  the  range  in  brightness  two  magnitudes.  Probably 


1 76  SYSTEMS  OF  STARS, 

the  change  in  brightness  is  continuous.  The  increase  of  light  is 
very  rapid,  occupying  not  more  than  one-fifth  of  the  whole  period. 
Jn  some  cases,  possibly  in  this  star,  the  light  remains  constant  for 
a  short  time  at  minimum.  In  most  cases,  however,  the  change  in 
brightness  seems  to  be  continuous.  The  simple  type  shown  by 
No.  74  is  more  prevalent  in  this  cluster  than  any  other.  There 
are,  nevertheless,  several  stars,  as  No.  7,  where  there  is  a  more  or 
less  well  marked  secondary  maximum.  The  period  of  this  star  is 
2d.  irh.  5im.  and  the  range  in  brightness  one  and  a  half  magni- 
tudes. The  light  curve  is  similar  to  that  of  well-known  short- 
period  variables,  as  Delta  Cephei  and  Eta  Aquilae.  Another  class 
may  be  represented  by  No.  126,  in  which  the  range  is  less  than  a 
magnitude  and  the  times  of  increase  and  decrease  are  about  equal. 
The  period  is  8h.  i2m.  3.  No.  24  may  perhaps  be  referred  to  as 
a  fourth  type.  The  range  is  about  seven-tenths  of  a  magnitude 
and  the  period  is  nh.  5111.  7.  Apparently  about  65  per  cent,  of 
the  whole  period  is  occupied  by  the  increase  of  the  light.  This 
very  slow  rate  of  increase  is  especially  striking  from  the  fact  that 
in  many  cases  in  this  cluster  the  increase  is  extremely  rapid, 
probably  not  more  than  10  per  cent,  of  the  whole  period.  In  one 
case,  No.  45,  having  a  period  of  14!!.  8m.,  the  rise  from  minimum 
to  maximum,  a  change  of  two  magnitudes,  takes  place  in  about 
one  hour,  and  in  certain  cases,  chiefly  owing  to  the  necessary 
duration  of  a  photographic  exposure,  there  is  no  proof  at  present 
that  the  rise  is  not  much  more  rapid." 

The  periods  of  63  of  the  85  variables  in  Messier  5 
have  been  determined  by  Professor  Bailey.  Their  most 
remarkable  feature  is  the  approach  of  a  majority  of 
them  to  half  a  day.  Of  the  number,  39,  or  more  than 
three-fifths,  are  contained  between  the  limits  loh. 
48m.  and  15!!. 

The  regularity  in  the  period  of  these  stars  is  re- 
markable. Several  have  been  studied  during  more 
than  a  thousand,  and  one  during  more  than  five 


STAR-CL  USTERS.  1 7  7 

thousand,  periods  without  irregularities  manifesting 
themselves. 

It  may  be  added  that  this  regularity  of  the  period, 
taken  in  connection  with  the  case  of  Eta  Aquilse,  al- 
ready mentioned,  affords  a  strong  presumption  that 
the  variations  in  the  light  of  these  stars  are  in  some 
way  connected  with  the  revolution  of  bodies  round 
them,  or  of  one  star  round  another.  Yet  it  is  certain 
that  the  types  are  not  of  the  Algol  class  and  that  the 
changes  are  not  due  merely  to  one  star  eclipsing  an- 
other. That  such  condensed  clusters  should  have  a 
great  number  of  close  binary  systems  is  natural,  al- 
most unavoidable,  we  might  suppose.  It  is  probable 
that  among  the  stars  in  general,  single  stars  are  the  ex- 
ception rather  than  the  rule.  If  such  be  the  case,  the 
rule  should  hold  yet  more  strongly  among  the  stars  of 
a  condensed  cluster. 

Perhaps  the  most  important  problem  connected 
with  clusters  is  the  mutual  gravitation  of  their  com- 
ponent stars.  Where  thousands  of  stars  are  con- 
densed into  a  space  so  small,  what  prevents  them  from 
all  falling  together  into  one  confused  mass  ?  Are  they 
really  doing  so,  and  will  they  ultimately  form  a  single 
body  ?  These  are  questions  which  can  be  satisfac- 
torily answered  only  by  centuries  of  observation  ;  they 
must,  therefore,  be  left  to  the  astronomers  of  the 
future. 


CHAPTER  XI 

NEBULAE 

Some  tumultuous  cloud 
Instinct  with  fire  and  nitre. 

MILTON. 

THE  first  nebula,  properly  so  called,  to  be  detected 
by  an  astronomical  observer  was  that  of  Orion. 
Huyghens,   in   his  Sy sterna  Saturnium,  gives  a  rude 
drawing  of  this  object,  with  the  following  description  : 

"  There  is  one  phenomenon  among  the  fixed  stars  worthy  of 
mention  which,  so  far  as  I  know,  has  hitherto  been  noticed  by  no 
one,  and,  indeed,  cannot  be  well  observed  except  with  large  tele- 
scopes. In  the  sword  of  Orion  are  three  stars  quite  close  to- 
gether. In  1656,  as  I  chanced  to  be  viewing  the  middle  one  of 
these  with  the  telescope,  instead  of  a  single  star,  twelve  showed 
themselves  (a  not  uncommon  circumstance).  Three  of  these  al- 
most touched  each  other,  and,  with  four  others,  shone  through  a 
nebula,  so  that  the  space  around  them  seemed  far  brighter  than 
the  rest  of  the  heavens,  which  was  entirely  clear,  and  appeared 
quite  black,  the  effect  being  that  of  an  opening  in  the  sky, 
through  which  a  brighter  region  was  visible." 

For  a  century  after  Huyghens  made  this  observa- 
tion it  does  not  appear  that  these  objects  received 
special  attention  from  astronomers.  The  first  to  ob- 
serve them  systematically  on  a  large  scale  was  Sir 

178 


NEBULA  179 

Wm.  Herschel,  whose  vast  researches  naturally  em- 
braced them  in  their  scope.  His  telescopes,  large 
though  they  were,  were  not  of  good  defining  power 
and,  in  consequence,  Herschel  found  it  impossible  to 
draw  a  certain  line  in  all  cases  between  nebulae  and 
clusters.  At  his  time  it  was  indeed  a  question  whether 
all  these  bodies  might  not  be  clusters.  This  question 
Herschel,  with  his  usual  sagacity,  correctly  answered 
in  the  negative.  Up  to  the  time  of  the  spectroscope, 
all  that  astronomers  could  do  with  nebulae  was  to  dis- 
cover, catalogue,  and  describe  them. 

Several  catalogues  of  these  objects  have  been  pub- 
lished. The  one  long  established  as  a  standard  is  the 
General  Catalogue  of  Nebula  and  Clusters,  by  Sir  John 
Herschel.  With  each  object  Herschel  gave  a  con- 
densed description.  Recently  Herschel's  catalogue 
has  been  superseded  by  the  general  catalogue  of 
Dreyer,  based  upon  it  and  published  in  the  Memoir? 
of  the  Royal  Astronomical  Society. 

Some  of  the  more  conspicuous  of  these  objects  are 
worthy  of  being  individually  mentioned.  At  the  head 
of  all  must  be  placed  the  great  nebula  of  Orion, 
This  is  plainly  visible  to  the  naked  eye  and  can  be  seen 
without  difficulty  whenever  the  constellation  is  visible. 
Note  the  three  bright  stars  lying  nearly  in  an  east 
and  west  line  and  forming  the  belt  of  the  warrior. 
South  of  these  will  be  seen  three  fainter  ones,  hang- 
ing below  the  belt,  as  it  were,  and  forming  the  sword. 
To  a  keen  eye,  which  sharply  defines  the  stars,  the 
middle  star  will  appear  hazy.  It  is  the  nebula  in 
question.  Its  character  will  be  strongly  brought  out 


i8o  NEBULAE 

by  the  smallest  telescope,  even  by  an  opera-glass. 
Drawings  of  it  have  been  made  by  numerous  astron- 
omers, the  comparison  of  which  has  given  rise  to  the 
question  whether  the  object  is  variable.  It  cannot  be 
said  that  this  question  is  yet  decided  ;  but  the  best 
opinion  would  probably  be  in  the  negative.  In  recent 
times  the  improvements  of  the  photographic  process 


THE  GREAT  NEBULA  OF  ORION,  AS  PHOTOGRAPHED  BY  A.  A.  COMMON,  F.R.S., 
WITH  HIS  FOUR-FOOT  REFLECTOR 

have  led  to  the  representation  of  the  object  by  photo- 
graphy. A  photograph  made  by  Mr.  A.  A.  Common, 
F.R.S.,  with  a  reflecting  telescope,  gives  so  excellent 
an  impression  of  the  object  that  by  his  consent  we  re- 
produce it. 

The  most  remarkable  feature  connected  with  the. 


NEBULA 


181 


nebula  of  Orion  is  the  so-called  Trapezium,  already 
described.  That  these  four  stars  form  a  system  by 
themselves  cannot  be  doubted.  The  darkness  of  the 
nebula  immediately  around  them  suggests  that  they 
were  formed  at  the  expense  of  the  nebulous  mass. 

Great  interest  has  recently  been  excited  in  the  spiral 
form  of  certain  nebulae.  The  great  spiral  nebula  M. 
5  i  in  Canes  Venatici  has  long  been  known.  We  re- 
produce a  photograph  of  this  object  and  another.  It 
is  found  by  recent  studies  at  the  Lick  Observatory 
that  a  spiral  form  can  be  detected  in  a  great  number 
of  these  objects  by  careful  examination. 


THE  GREAT  SPIRAL  NEBULA  M.  51.  AS  PHOTOGRAPHED  WITH  THE 
CROSSLEY  REFLECTOR  AT  THE  LICK  OBSERVATORY 


1 82  NEBULAE 

Another  striking  feature  of  numerous  nebulae  is 
their  varied  and  fantastic  forms,  of  which  we  give  a 
number  of  examples.  The  "  Trifid  nebula,"  figured 
in  our  frontispiece,  is  a  noted  one  in  this  respect. 

The  great  nebula  of  Andromeda  is  second  only  to 
that  of  Orion.  It  also  is  plainly  visible  to  the  naked 
eye  and  can  be  more  readily  recognised  as  a  nebula 


THE  GREAT  NEBULA  OF  ANDROMEDA,  PHOTOGRAPHED  BY 
DR.  ISAAC  ROBERTS,  F.  R.S. 


NEBULAE  183 

than  can  the  other.  It  has  frequently  been  mistaken 
for  a  comet.  Seen  through  a  telescope  of  high  power, 
its  aspect  is  singular,  as  if  a  concealed  light  were 
seen  shining  through  horn  or  semi-transparent  glass. 

Another  nebula  which,  though  not  conspicuous  to 
the  naked  eye,  has  attracted  much  attention  from  as- 
tronomers, is  known,  from  the  figure  of  one  of  its 
branches,  as  the  Omega  nebula.  Sir  John  Herschel, 
who  first  described  this  object  in  detail,  says  of  it  : 
"  The  figure  is  nearly  that  of  the  Greek  capital 
Omega,  somewhat  distorted  and  very  unequally 
bright."  From  one  base  of  the  letter  extends  out  to 
the  east  a  long  branch  with  a  hook  at  the  end,  which 
in  most  of  the  drawings  is  more  conspicuous  than  the 
portion  included  in  the  Omega.  The  drawings,  how- 
ever, vary  so  much  that  the  question  has  been  raised 
whether  changes  have  not  taken  place  in  the  object. 
As  in  other,  cases,  this  question  is  one  which  it  is  not 
yet  possible  to  decide.  The  appearance  of  such  ob- 
jects varies  so  much  with  the  aperture  of  the  telescope 
and  the  conditions  of  vision  that  it  is  not  easy  to  de- 
cide whether  the  apparent  change  may  not  be  due  to 
these  causes.  It  is  curious  that  in  a  recent  photo- 
graph, the  Omega  element  of  it,  if  I  may  use  the 
term,  is  far  less  conspicuous  than  in  the  older  draw- 
ings, and  is,  in  fact,  scarcely  recognisable. 

Among  the  most  curious  of  the  nebulae  are  the 
annular  ones,  which,  as  the  term  implies,  have  the 
form  of  a  ring.  It  should  be  remarked  that  in  such 
cases  the  interior  of  the  ring  is  not  generally  entirely- 
black,  but  is  filled  with  nebulous  light.  We  may, 


1 84  NEBULAE 

therefore,  define  these  objects  as  nebulae  which  are 
brighter  round  their  circumference  than  in  the  centre. 
The  most  striking  of  the  annular  nebulae  is  that  of 
Lyra.  It  may  easily  be  found  from  being  situated 
about  half-way  between  the  stars  Beta  and  Gamma. 
Although  it  is  visible  in  a  medium  telescope,  it 
requires  a  powerful  one  to  bring  out  its  peculiar  feat- 
ures in  a  striking  way.  Recently  it  has  been  photo- 
graphed by  Keeler  with  the  Crossley  reflector  of  the 
Lick  Observatory,  who  found  that  the  best  general 
impression  was  made  with  an  exposure  of  only  ten 
minutes. 

The  ring,  as  shown  by  Keeler's  photograph,  has  a 
quite  complicated  structure.  It  seems  to  be  made  up 
of  several  narrower  bright  rings,  interlacing  somewhat 
irregularly,  the  spaces  between  them  being  filled  with 
fainter  nebulosity.  One  of  these  rings  forms  the 
outer  boundary  of  the  preceding  end  of  the  main 
ring.  Sweeping  around  to  the  north  end  of  the 
minor  axis,  it  becomes  very  bright,  perhaps  by  super- 
position on  the  broader  main  ring  of  the  nebula  at  this 
place.  It  crosses  this  ring  obliquely,  forming  the 
brightest  part  of  the  whole  nebula,  and  then  forms  the 
inner  boundary  of  the  main  ellipse  toward  its  follow- 
ing end.  The  remaining  part  of  the  ring  is  not  so 
easily  traced,  as  several  other  rings  interlace  on  the 
south  end  of  the  ellipse. 

The  central  star  of  this  nebula  has  excited  some  in- 
terest. Its  light  seems  to  have  a  special  actinic 
power,  as  the  star  is  more  conspicuous  on  the  photo- 
graphs than  to  the  eye. 


NEBULA  185 

There  are  several  other  annular  nebulae  which  are 
fainter  than  that  of  Lyra.  The  one  best  visible  in  our 
latitudes  is  known  as  H  IV.  13,  or  4565  of  Dreyer's 
catalogue.  It  is  situated  in  the  constellation  Cygnus, 
which  adjoins  Lyra.  Both  Herschel  and  Lord  Rosse 
have  made  drawings  of  it.  It  was  photographed  by 
Keeler  with  the  Crossley  reflector  on  the  nights  of 
August  9  and  10,  1899,  with  exposures  of  one  and  two 
hours,  respectively.  Keeler  states  that  the  nebula,  as 
shown  by  these  photographs,  "  is  an  elliptical,  nearly 
circular  ring,  not  quite  regular  in  outline,  pretty 
sharply  denned  at  the  outer  edge."  The  outside  dimen- 
sions are  : 

Major  axis 42".$ 

Minor  axis 4°-"5 

Position  angle  of  major  axis 32°. 

The  nebula  has  a  nucleus  with  a  star  exactly  in  the 
center.  This  is  very  conspicuous  on  a  photograph, 
but  barely  if  at  all  visible  with  a  36-inch  reflector. 

Another  curious  class  of  nebulae  are  designated  as 
planetary,  on  account  of  their  form.  These  consist  of 
minute,  round  disks  of  light,  having  somewhat  the  ap- 
pearance of  a  planet.  The  appellation  was  suggested 
by  this  appearance.  These  objects  are  for  the  most 
part  faint  and  difficult. 

It  is  impossible  to  estimate  the  number  of  nebulae 
in  the  heavens.  New  ones  have  from  time  to  time 
been  discovered,  located,  and  described  by  many  ob- 
servers during  the  last  thirty  years.  Among  these 


1 86  NEBULA 

Lewis  Swift  is  worthy  of  special  mention  as  one  of  the 
most  successful  discoverers  of  these  objects. 


NEBULOUS  MASS  IN  CYQNUS,   INCLUDING  H.  V.  14  AND  H.  2093, 
PHOTOGRAPHED  AT  THE   LICK  OBSERVATORY 

But  in  recent  times  photography  has  gone  far  to- 
ward replacing  the  eye  in  this  field.  On  photographing 
the  sky  near  the  galactic  pole  with  the  Crossley  reflec- 
tor, Keeler  found  no  less  than  seven  of  these  objects 
in  a  space  of  about  one-half  a  square  degree.  He  there- 


NEBULAE  187 

fore  estimates  the  whole  number  in  the  heavens 
capable  of  being  photographed  at  several  hundred 
thousand.  It  may  be  assumed  that  only  a  moderate 
fraction  of  these  are  visible  to  the  eye,  even  aided  by 
the  largest  telescopes. 

Among  the  most  singular  of  these  objects  are  large 
diffused  nebulae,  sometimes  extending  through  a  re- 
gion of  several  degrees.  A  number  of  these  were 
discovered  by  Herschel.  Barnard,  W.  H.  Pickering, 
and  others  have  photographed  these  for  us.  One  of 
the  most  remarkable  of  them  winds  around  in  the 
constellation  Orion  in  such  away  that  at  first  sight  one 
might  be  disposed  to  inquire  whether  the  impression 
on  the  photographic  plate  might  not  have  been  the  re- 
sult of  some  defect  in  the  apparatus  or  some  reflection 
of  the  light  of  the  neighbouring  stars,  which  is  so  apt 
to  occur  in  these  delicate  photographic  operations. 
But  its  existence  happens  to  be  completely  confirmed 
by  independent  testimony.  It  was  first  detected  by 
VV.  H.  Pickering  and  afterwards  independently  by 
Barnard. 

A  curious  fact  connected  with  the  distribution  of 
nebulae  over  the  sky  is  that  it  is  in  a  certain  sense  the 
reverse  of  that  of  the  stars.  The  latter  are  vastly 
more  numerous  in  the  regions  near  the  Milky  Way 
and  fewer  in  number  near  the  poles  of  that  belt.  But 
the  reverse  is  the  case  with  the  nebulae  proper.  They 
are  least  numerous  in  the  Milky  Way  and  increase  in 
number  as  we  go  from  it  in  either  direction.  Precisely 
what  this  signifies  one  would  not  at  the  present  time 
be  able  to  say.  Perhaps  the  most  obvious  suggestion 


1 88  NEBULAE 

would  be  that  in  these  two  opposite  nebulous  regions 
the  nebulae  have  not  yet  condensed  into  stars.  This, 
however,  woul.d  be  a  purely  speculative  explanation. 

On  the  other  hand,  star-clusters  are  more  numerous 
in  the  galactic  region.  This,  however,  is  little  more 
than  saying  that  in  the  regions  where  the  stars  are  so 
much  more  numerous  than  elsewhere  many  of  them 
naturally  tend  to  collect  in  clusters.  It  is,  however,  a 
curious  fact  that,  so  far  as  has  yet  been  noticed,  the 
large  diffused  nebulae  which  we  have  mentioned  are 
more  numerous  in  or  near  the  Milky  Way.  If  this 
tendency  is  established  it  will  mark  a  curious  distinc- 
tion between  them  and  the  smaller  nebulae. 

The  most  interesting  question  connected  with  these 
objects  is  that  of  their  physical  constitution.  When, 
about  1866,  the  spectroscope  was  first  applied  to  as- 
tronomical investigation  by  Huggins  he  found  that 
the  light  of  the  great  nebula  of  Orion  formed  a  spec- 
trum of  bright  lines,  thus  showing  the  object  to  be 
gaseous.  This  was  soon  found  to  be  true  of  the  ne- 
bulae generally.  There  is,  however,  a  very  curious 
exception  in  the  case  of  the  great  nebula  of  Androm- 
eda. This  object  gives  a  more  or  less  continuous 
spectrum.  The  bright  lines  in  the  spectrum  of  a  ne- 
bula are  seldom  or  never  more  than  four  in  number. 
The  wave-lengths  are  4341,  4861,  4957,  5004.  The 
first  of  these  is  the  violet,  is  very  faint,  and  visible  only 
in  the  brightest  nebulae.  The  last  is  the  brightest, 
and  in  faint  nebulae  is  the  only  one  that  can  be  dis- 
tinguished. None  of  these  lines  can  be  certainly 
identified  with  those  of  any  terrestrial  substance. 


NEBULAE  189 

The   supposed    matter    which    produces   them   has, 
therefore,  been  called  nebulum. 

Beyond  the  general  fact  that  the  light  of  a  nebula 
does  not  come  from  solid  matter,  but  from  matter  of 
a  gaseous  or  other  attenuated  form,  we  have  no  cer- 
tain knowledge  of  the  physical  constitution  of  these 
bodies.  Certain  features  of  their  constitution  can, 
however,  be  established  with  a  fair  approach  to  accu- 
racy. Not  only  the  spectroscopic  evidence  of  bright 
lines  but  the  aspect  of  the  objects  themselves  show 
that  they  are  transparent  through  and  through.  This 
is  remarkable  when  taken  in  connection  with  their  in- 
conceivable size.  Leaving  out  the  large  diffused 
nebulse  which  we  have  mentioned,  these  objects  are 
frequently  several  minutes  in  diameter.  Of  their  dis- 
tance we  know  nothing,  except  that  they  are  probably 
situated  in  the  distant  stellar  regions.  Their  parallax 
can  be  but  a  small  fraction  of  a  second.  We  shall 
probably  err  greatly  in  excess  if  we  assume  that  it 
varies  between  one-hundredth  and  one-tenth  of  a 
second.  To  assign  this  parallax  is  the  same  thing  as 
saying  that  at  the  distance  of  the  nebulse  the  dimen- 
sions of  the  earth's  orbit  would  show  a  diameter  which 
might  range  between  one-fiftieth  and  one-fifth  of  a 
second,  while  that  of  Neptune  would  be  more  or  less 
than  one  second.  Great  numbers  of  these  objects 
are,  therefore,  thousands  of  times  the  dimensions  bf 
the  earth's  orbit,  and  probably  most  of  them  are  thou- 
sands of  times  the  dimensions  of  the  whole  solar 
system.  That  they  should  be  completely  trans- 
parent through  such  enormous  dimensions  shows 


i9o  NEBULA 

their  extreme  tenuity.  Were  our  solar  system  placed 
in  the  midst  of  one  of  them,  it  is  probable  that  we 
should  not  be  able  to  find  any  evidence  of  its  existence. 

A  form  of  matter  so  different  from  any  that  can  be 
found  or  produced  on  the  surface  of  the  earth  can 
hardly  be  explained  by  our  ordinary  views  of  matter. 
A  theory  has,  however,  been  propounded  by  Sir  Nor- 
man Lockyer,  so  ingenious  as  to  be  at  least  worthy  of 
mention.  It  is  that  these  objects  are  vast  collections 
of  meteorites  in  rapid  motion  relatively  to  each  other, 
which  come  into  constant  collision.  Their  velocity  is 
such  that  at  each  collision  heat  and  light  are  produced. 
In  the  language  of  our  progenitors,  who  in  the  ab- 
sence of  matches  used  flint  and  steel,  they  "  strike  fire  " 
against  each  other.  The  idea  of  such  a  process  orig- 
inated with  Prof.  P.  G.  Tait,  in  an  attempt  to  explain 
the  tail  of  a  comet,  but  it  was  elaborated  and  devel- 
oped by  Mr.  Lockyer  in  his  work  on  the  Meteor itic 
Theory. 

The  objections  to  this  theory  seem  insuperable.  A 
velocity  so  great,  at  such  a  distance  from  the  centre 
of  the  nebulae,  would  be  incompatible  with  the  extreme 
tenuity  of  these  objects.  Every  time  that  two  meteors 
came  into  collision  they  would  lose  velocity,  and,  there- 
fore, if  the  mass  was  sufficient  to  hold  them  from  flying 
through  space,  would  rapidly  fall  toward  a  common 
centre.  The  amount  of  light  produced  by  the  collision 
of  two  such  objects  is  only  a  minute  fraction  of  the  en- 
ergy lost.  The  meteors  which  fall  on  the  earth  are  most- 
ly of  iron,  and,  were  the  theory  true,  numerous  lines  of 
iron  should  be  most  conspicuous  in  the  spectrum. 


CHAPTER   XII 
CONSTITUTION  OF  THE  STARS 

Doubt  thou  the  stars  are  fire. — SHAKESPEARE. 

THE  spectroscope  shows  that,  although  the  consti- 
tution of  the  stars  offers  an  infinite  variety  of  de- 
tail, we  may  say,  in  a  general  way,  that  these  bodies 
are  suns.  It  would,  perhaps,  be  more  correct  to  say 
that  the  sun  is  one  of  the  stars  and  does  not  differ  es- 
sentially from  them  in  its  constitution.  The  problems 
of  the  physical  constitution  of  the  sun  and  stars  may, 
therefore,  be  regarded  as  one,  all  these  being  bodies 
of  the  same  general  nature,  consisting  of  vast  masses 
of  incandescent  matter  at  so  exalted  a  temperature 
as  to  shine  by  their  own  light. 

This  similarity  in  general  constitution  does  not, 
however,  preclude  very  great  differences  in  detail. 
The  spectra  of  the  stars  show  that  hardly  Diversities 
any  two  are  exactly  alike  in  the  substances  among 
of  which  they  are  composed,  and  in  the  the  star;5- 
temperature  and  density  of  these  substances.  Most 
remarkable  is  the  diversity  of  their  actual  luminosities 
or  the  amount  of  light  and  heat  which  they  individu- 
ally emit.  The  whole  tendency  of  recent  research 
has  been  to  accentuate  this  diversity.  It  was  once 


1 92  CONSTITUTION  OF  THE  STARS 

supposed  that  the  brighter  stars  must  all  be  among  the 
nearer  ones  to  us.  But  as  parallaxes  were  measured 
with  greater  and  greater  accuracy,  it  became  more  and 
more  certain  that  this  is  not  always  the  case. 

The  last  step  in  this  direction  has  been  taken  by  Gill 
in  his  measures  of  the  parallaxes  of  the  southern  stars 
of  the  first  magnitude.  Of  two  at  least,  Canopus  and 
Rigel,  the  parallaxes  are  so  small  as  to  elude  certain 
detection.  Most  extraordinary  is  the  case  of  Canopus> 
the  second  brightest  star  in  the  heavens.  A  long-con- 
tinued series  of  measures,  sufficient  to  make  evident  a 
parallax  of  one  hundredth  of  a  second,  converged  to  a 
value  of  o".ooo  !  Canopus  is  doubtless  situated  among 
the  small  stars  of  the  eighth  magnitude  around  it,  of 
which  we  have  every  reason  to  believe  the  parallax  to 
be  only  a  few  thousandths  of  a  second.  In  all  likeli- 
iiood,  it  is  more  than  ten  thousand  times  as  bright  as 
the  sun.  A  planet  as  near  to  it  as  we  are  to  the  sun 
would  become  red  hot  under  its  radiation. 

At  the  other  extreme  we  have  the  minute  stars  of 
large  proper  motion  whose  parallaxes  have  been  meas- 
ured. These  seem  to  be  of  only  about  one-fiftieth 
the  brightness  of  the  sun.  It  therefore  seems  certain 
that  some  stars  emit  hundreds  of  thousands — nay, 
millions  of  times  as  much  light  as  others. 

It  has  long  been  known  that  the  mean  density  of  the 
sun  is  only  one-fourth  that  of  the  earth,  and,  there- 
Masses  and  f°re'  IGSS  than  nalf  as  much  again  as  that  of 
Densities  of  water.  In  a  few  cases  an  approximate  es- 

stars-  timate  of  the  density  of  stars  may  be  made. 
The  method  by  which  this  is  done  can  be  rigorously 


MASSES  AND  DENSITIES  OF  THE  STAKS   193 

set  forth  only  by  the  use  of  algebraic  formulae,  but  a 
general  idea  of  it  can  be  obtained  without  the  use  of 
that  mode  of  expression. 

Let  us  set  forth  in  advance  an  extension  of  Kepler's 
third  law,  which  applies  to  every  case  of  two  bodies  re- 
volving around  each  other  by  their  mutual  gravitation 
The  law  in  question,  as  stated  by  Kepler,  is  that  the 
cubes  of  the  mean  distances  of  the  planets  are  propor- 
tional to  the  squares  of  their  times  of  revolution.  If  we 
suppose  the  mean  distances  to  be  expressed  in  terms  of 
the  earth's  mean  distance  from  the  sun  as  a  unit  of 
length,  and  if  we  take  the  year  as  the  unit  of  time, 
then  the  law  may  be  expressed  by  saying  that  the 
cubes  of  the  mean  distances  will  be  equal  to  the 
squares  of  the  periods.  For  example,  the  mean  dis- 
tance of  Jupiter  is  thus  expressed  as  5.2.  If  we  take 
the  cube  of  this,  which  is  about  140,  and  then  extract 
the  square  root  of  it,  we  shall  have  n.8,  which  is  the 
period  of  revolution  of  Jupiter  around  the  sun  ex- 
pressed in  years.  If  we  cube  9.5,  the  mean  distance 
of  Saturn,  we  shall  have  the  square  of  a  little  more 
than  29,  which  is  Saturn's  time  of  revolution. 

We  may  also  express  the  law  by  saying  that  if  we 
divide  the  cube  of  the  mean  distance  of  any  planet  by 
the  square  of  its  periodic  time  we  shall  always  get  i 
as  a  quotient. 

The  theory  of  gravitation  and  the  elementary 
principles  of  force  and  motion  show  that  a  similar  rule 
is  true  in  the  case  of  any  two  bodies  revolving  around 
each  other  in  virtue  of  their  mutual  gravitation.  If  we 
divide  the  cube  of  their  mean  distance  apart  by  the 


194  CONSTITUTION  OF  THE  STARS 

square  of  their  time  of  revolution,  we  shall  get  a 
quotient  which  will  not  indeed  be  i,  but  which  will 
be  a  number  expressing  the  combined  mass  of  the  two 
bodies.  If  one  body  is  so  small  that  we  leave  its  mass 
out  of  consideration,  then  the  quotient  will  express  the 
mass  of  the  larger  body.  If  the  latter  has  several 
minute  satellites  moving  around  it,  the  quotients  will 
be  equal,  as  in  the  case  of  the  sun,  and  will  express 
the  mass  of  this  central  body.  If,  as  in  the  case  we 
have  supposed,  we  take  the  year  as  a  unit  of  time  and 
the  distance  of  the  earth  from  the  sun  as  a  unit  of 
length,  the  quotient  will  express  the  mass  of  the  cen- 
tral body  in  terms  of  the  mass  of  the  sun.  It  is  thus 
that  the  masses  of  the  planets  are  determined  from  the 
periodic  times  and  distances  of  their  satellites,  and  the 
masses  of  binary  systems  from  their  mean  distance 
apart  and  their  periods.  To  express  the  general  law 
by  a  formula  we  put 

a,  the  mean  distance  apart  of  the  two  bodies,  or  the 
semi-major  axis  of  their  relative  orbit  in  terms  of  the 
earth's  mean  distance  from  the  sun  ; 

P,  their  periodic  time  ; 

M,  their  combined  mass  in  terms  of  the  sun's  mass 
as  unity. 

Then  we  shall  have  : 


Another  conclusion  we  draw  is  that  if  we  know  the 
time  of  revolution  and  the  radius  of  the  orbit  of  any 
binary  system,  we  can  determine  what  the  time  of 


MASSES  AND  DENSITIES  OF  THE  STARS   195 

revolution  would  be  if  the  radius  of  the  orbit  had 
some  standard  length,  say  unity.  To  do  this  we  have 
only  to  divide  the  actual  period  by  the  cube  of  the 
square  root  of  the  actual  radius  of  the  orbit. 

We  cannot  determine  the  dimensions  of  a  binary 
system  unless  we  know  its  distance  from  us.  But 
there  is  a  remarkable  law  which,  so  far  as  I  know, 
was  first  announced  by  Pickering,  by  virtue  of  which 
we  can  determine  a  certain  relation  between  the  sur- 
face brilliancy  and  the  density  of  a  binary  system 
without  knowing  its  distance. 

Let  us  suppose  a  number  of  bodies  of  the  same  con- 
stitution and  temperature  as  the  sun  —  models  of  the 
latter  we  may  say — differing  from  it  only  in  size.  To 
fix  the  ideas,  we  shall  suppose  two  such  bodies,  one 
having  twice  the  diameter  of  the  other.  Being  of  the 
same  brilliancy,  we  suppose  them  to  emit  the  same 
amount  of  light  per  unit  of  surface.  The  larger  body, 
having  four  times  the  surface  of  the  smaller,  will  then 
emit  four  times  as  much  light.  The  volumes  being 
proportional  to  the  cubes  of  their  diameters,  it  will 
have  eight  times  its  volume.  The  densities  being* 
supposed  equal,  it  will  have  eight  times  the  mass. 

Suppose  that  each  has  a  satellite  revolving  around 
it,  of  which  the  size  is  proportional  to  that  of  its  pri- 
mary, as  shown  in  the  figure,  and  that  the  orbit  of  the 
satellite  of  the  larger  body  is  twice  the  radius  of  that 
of  the  smaller  one.  Calling  the  radius  of  the  nearer 
satellite  i,  that  of  the  more  distant  one  will  then  be  2, 
The  cube  of  this  number  is  8.  It  follows  from  the  ex- 
tension of  Kepler's  third  law,  which  we  have  cited 


196  CONSTITUTION  OF  THE  STARS 

that  the  times  of  revolution  of  the  two  satellites  will 
be  the  same.  Thus  the  two  bodies,  A  and  B,  with 
their  satellites,  a  and  b,  form  two  binary  systems  whose 
proportions  and  whose  periods  are  the  same,  only  the 
linear  dimensions  of  B  are  all  double  those  of  A.  In 
other  words,  we  shall  have  a  pair  of  binary  systems 
which  will  look  alike  in  every  respect,  only  one  will 
have  double  the  dimensions  and  eight  times  the  mass 
of  the  other. 


TWO  BINARY  SYSTEMS  ON  THE  SAME  MODEL,  ONE  HAVING  TWICE  THE 
LINEAR  DIMENSIONS  OF  THE  OTHER 

Now,  let  us  suppose  the  larger  system  to  be  placed 
twice  as  far  away  from  us  as  the  smaller.  The  two 
will  then  appear  of  the  same  size,  and,  if  stars,  will  ap- 
pear of  the  same  brightness,  while  the  two  orbits  will 
have  the  same  apparent  dimensions.  In  a  word,  the 
two  systems  will  appear  alike  when  examined  with 
the  telescope,  and  the  periodic  times  will  be  equal. 

Near  the  end  of  the  second  chapter  we  have  given 
a  little  table  showing  the  magnitude  that  the  sun 
would  appear  to  us  to  have  were  it  placed  at  dif- 
ferent distances  among  the  stars.  The  parallaxes  we 


MASSES  AND  DENSITIES  OF  THE  STARS   197 

have  there  given  are  simply  the  apparent  angles 
which  would  be  subtended  by  the  radius  of  the 
earth's  orbit  at  different  distances.  It  follows  that, 
were  the  stars  all  of  similar  constitution  to  the  sun, 
the  numbers  given  in  the  last  column  of  the  table  re- 
ferred to  would,  in  all  cases,  express  the  apparent  dis- 
tance from  the  star  of  a  companion,  having  a  time  of 
revolution  of  one  year.  From  this  we  may  easily 
show  what  would  be  the  time  of  revolution  of  any 
binary  system  of  which  the  companions  were  separated 
by  i",  if  the  stars  were  of  the  same  constitution  as  the 
sun. 

Periods  of  binary  systems  whose  components  are  separated  by  i"  and 
whose  constitution  is  the  same  as  that  of  the  sun. 

Period,  Annual 

Mag.  Years.  Motion. 

I 1 .8  200° 

2 3-5  I02 

3 7-0  51 

4 • i4-i  25 

5 28.1  J3 

6 56.0                            6 

7 112.  3.2 

8 223.                              1.6 

It  will  be  seen  that  the  periods  are  very  nearly 
doubled  for  each  diminution  of  the  brilliancy  of  the 
star  by  one  magnitude.  Moreover,  the  value  of  the 
photometric  ratio  for  two  consecutive  magnitudes  is  a 
little  uncertain,  so  that  we  may,  without  adding  to  the 
error  of  our  results,  suppose  the  period  to  be  exactly 
doubled  for  each  addition  of  unity  to  the  magnitude. 
A  computation  of  the  period  for  any  magnitude,  m,  may 
be  made  with  all  necessary  precision  by  the  formula  : 


198  CONSTITUTION  OF  THE  STARS 

P=oy.88  X   2m; 
or,         log.  P=Q.944  +  o.$m. 

It  will  now  be  of  interest  to  compare  the  results  of 
this  theory  with  the  observed  periods  of  binary  sys- 
tems with  a  view  to  comparing  their  constitution  with 
that  of  our  sun.  There  are,  however,  two  difficulties 
in  the  way  of  doing  this  with  precision. 

The  first  difficulty  is  that  there  are  very  few  binary 
systems  of  which  the  apparent  dimensions  of  the  orbits 
and  the  periods  are  known  with  any  approach  to  ex- 
actness. This  would  not  be  a  serious  matter  were  it 
not  that  the  systems  of  short,  and,  therefore,  known, 
periods  belong  to  a  special  class,  that  having  the 
greatest  density.  Hence,  when  we  derive  our  results 
from  such  systems  we  shall  be  making  a  biassed  selec- 
tion from  this  particular  class  of  stars. 

The  next  difficulty  is  that  the  theory  which  we  have 
set  forth  assumes  the  mass  of  the  satellite  either  to  be 
very  small  compared  with  that  of  the  star,  or  the  two 
bodies  to  be  of  the  same  constitution.  If  we  apply 
the  theory  to  systems  in  which  this  is  not  the  case,  the 
results  which  we  shall  get  will  be,  in  a  certain  way, 
those  corresponding  to  the  mean  of  the  two  compo- 
nents. Were  it  a  question  of  masses,  we  should  get 
with  entire  precision  the  sum  of  the  masses  of  the  two 
bodies.  The  best  we  can  do,  therefore,  is  to  suppose 
the  two  companions  fused  into  one  having  the  com- 
bined brilliancy  of  the  two.  Then,  if  the  result  is  too 
small  for  one,  it  will  be  too  large  for  the  other. 

To  show  the  method  of  proceeding,   I  have  taken 


MASSES  AND  DENSITIES  OF  THE  STARS   199 


the  six  systems  of  shortest  period  found  in  Dr.  See's 
Researches  on  Stellar  Evolution.  The  principal 
numbers  are  shown  in  the  table  below. 

The  first  column,  a",  after  the  name  of  the  star, 
gives  the  apparent  semi-major  axis  of  the  orbit  in 
seconds  of  arc.  The  next  column  gives  the  period  in 
years.  Column  Mag.  gives  the  apparent  magnitude 
which  the  system  would  have  were  the  two  bodies 
fused  into  one.  Column  P'  gives  the  period  in  years 
as  it  would  be  were  the  radius  of  the  orbit  equal  to 
one  second.  It  is  formed  by  dividing  the  actual 
period  by  a"^.  The  next  column  gives  the  period  as 
it  would  be  were  the  stars  of  similar  constitution  to 
the  sun.  The  last  column  gives  the  square  of  the 
ratio  of  the  two  periods,  which,  if  the  stars  had  the 
same  surface  brilliancy  as  the  sun,  would  express 
the  ratio  of  density  of  the  stars  to  that  of  the  sun. 
Actually,  it  gives  the  product :  Density  X  brilliancy  j. 


A" 

PER. 

MAG. 

p' 

SUN'S 

PER. 

STAR'S 

DENSITY. 

Jt  Peo'asi 

o    4.2 

Years. 
114 

4  2 

Years. 
41  Q 

Years. 
l6  2 

O  1C 

<?  Equulei  

o  .45 

1  1.4 

4.6 

37.8 

2I.O 

O.tl 

£  Sagittarii   

o  .60 

188 

2.9 

32.7 

6  7 

o  04 

P°o  Argus        .        . 

o  .61; 

22  O 

e  t 

42  O 

•2Q    7 

O  QO 

42  Comae  

o  .64 

2S.6 

4-4 

So.o 

18  q 

O  14 

ft  Delphini      

o  .67 

27  7 

7  7 

qo  4 

114 

O  C  I 

The  numbers  in  the  last  column  being  all  less  than 
unity,  it  follows  that  either  these  stars  are  much  less 
dense  than  the  sun  or  they  are  of  much  greater  sur- 
face brilliancy.  Moreover,  these  stars  belong  to  a 


200  CONSTITUTION  OF  THE  STARS 

selected  list  in  which  the  numbers  of  the  last  column 
are  larger  than  the  average. 

To  form  some  idea  of  the  result  of  a  selection  from 
the  stars  in  general,  we  may  assume  that  the  average 
of  all  the  measured  distances  between  the  components 
of  a  number  of  binary  systems  is  equal  to  the  average 
radius  of  their  orbits,  and  that  the  observed  annual 
motion  is  equal  to  the  mean  motion  of  the  companion 
in  its  orbit.  Taking  a  number  of  cases  of  this  sort,  I 
find  that  the  number  corresponding  to  the  last  num- 
ber of  the  preceding  table  would  be  little  more  than 
one-thousandth. 

A  very  remarkable  case  is  that  of  Zeta  Orionis. 
This  star,  in  the  belt  of  Orion,  is  of  the  second  mag- 
nitude. It  has  a  minute  companion  at  a  distance  of 
2".5.  Were  it  a  model  of  the  sun,  a  companion  at 
this  apparent  distance  should  perform  its  revolution  in 
fourteen  years.  But,  as  a  matter  of  fact,  the  motion 
is  so  slow  that  even  now,  after  fifty  years  of  observa- 
tion, it  cannot  be  determined  with  any  precision.  It 
is  probably  less  than  o°.  i  in  a  year.  The  number  ex- 
pressing the  comparison  of  the  density  and  surface 
brilliancy  of  this  star  with  those  of  the  sun  is  probably 
less  than  .0001. 

The  general  conclusion  to  be  drawn  is  obvious. 
The  stars  in  general  are  not  models  of  our  sun,  but 
have  a  much  smaller  mass  in  proportion  to  the  light 
they  give  than  our  sun  has.  They  must,  therefore, 
have  either  a  less  density  or  a  greater  surface 
brilliancy. 

We  may  now  inquire  whether  such  extreme  differ- 


MASSES  AND  DENS I TIES  OF  THE  STAKS  201 

ences  of  surface  brilliancy  or  of  density  are  more 
likely.  The  brilliancy  of  a  star  depends  primarily, 
not  on  its  temperature  throughout,  but  on  that  of 
some  region  near  or  upon  its  surface.  The  tempera- 
ture of  this  surface  cannot  be  kept  up  except  by  con- 
tinual convection  currents  from  the  interior  to  the 
surface.  We  are,  therefore,  to  regard  the  amount  of 
light  emitted  by  a  star  not  merely  as  indicating  tem- 
perature, but  as  limited  by  the  quantity  of  matter 
which,  impeded  by  friction,  can  come  up  to  the  surface, 
and  there  cool  off  and  afterwards  sink  down  again. 
This  again  depends  very  largely  on  internal  friction, 
and  is  limited  by  that.  Owing  to  this  limitation,  we 
cannot  attribute  the  difference  in  question  wholly  to 
surface  brilliancy.  We  must  conclude  that  at  least 
the  brighter  stars  are,  in  general,  composed  of  matter 
much  less  dense  than  that  of  the  sun.  Many  of  them 
are  probably  even  less  dense  than  air  and  in  nearly  all 
cases  the  density  is  far  less  than  that  of  any  known 
liquid. 

An  ingenious  application  of  the  mechanical 
principle  we  have  laid  down  has  been  made  independ- 
ently by  Mr.  A.  W.  Roberts,  of  South  Africa,  and  Mr. 
H.  N.  Russell,  of  Princeton,  in  another  way.  If  we 
only  knew  the  relation  between  the  diameters  of  the 
two  companions  of  a  binary  system,  and  its  dimensions, 
we  could  decide  how  much  of  the  difference  in  ques- 
tion is  due  to  density  and  how  much  to  surface  bril- 
liancy. Now  this  may  be  approximately  done  in  the 
case  of  variable  stars  of  the  Algol  and  Beta  Lyrae 
types.  If,  as  is  probably  the  most  common  case,  the 


202  CONSTITUTION  OF  THE  STARS 

passage  of  the  stars  over  each  other  is  nearly  cen- 
tral, the  ratio  of  their  diameter  to  the  radius  of  the 
orbit  may  be  determined  by  comparing  the  duration 
of  the  eclipse  with  the  time  of  revolution.  This  was 
one  of  the  fundamental  data  used  by  Myers  in  his 
work  on  Beta  Lyrse,  of  which  we  have  quoted  the  re- 
sults. Without  going  into  reasoning  or  technical  de- 
tails at  length,  we  may  give  the  results  reached  by 
Roberts  and  Russell  in  the  case  of  the  Algol  variables. 

For  the  variable  star  X  Carinse,  Roberts  finds,  as  a 
superior  limit  for  the  density  of  the  star  and  its  com- 
panion, one-fourth  the  density  of  the  sun.  It  may  be 
less  than  this  is,  to  any  extent. 

In  the  case  of  S  Velorum  the  superior  limits  of  den- 
sity are : 

Bright  star 0.61 

Companion 0.03 

In  the  case  of  RS  Sagittarii  the  upper  limits  of  den- 
sity are  o.  16  and  0.21. 

It  is  possible,  in  the  mean  of  a  number  of  cases  like 
these,  to  estimate  the  general  average  amount  by 
which  the  densities  fall  below  the  limits  here  given. 
Roberts's  final  conclusion  is  that  the  average  density 
of  the  Algol  variables  and  their  eclipsing  companions 
is  about  one-eighth  that  of  the  sun. 

The  work  of  Russell  was  carried  through  at  the 
same  time  as  that  of  Roberts,  and  quite  independ- 
ently of  his.  It  appeared  at  the  same  time.1  His 
formulae  and  methods  were  different,  though  they 

1  Astrophysical  yournal,  vol.  x,  no.  5. 


MASSES  AND  DENSITIES  OF  THE  STARS   203 

rested  on  similar  fundamental  principles.  Taking  the 
density  of  the  sun  as  unity,  he  computes  the  superior 
limit  of  density  for  12  variables,  based  on  their  periods 
and  the  duration  of  their  partial  eclipses.  The 
greatest  limit  is  in  the  case  of  Z  Herculisand  is  0.728. 
The  least  is  in  the  case  of  S  Cancri  and  is  0.035. 
The  average  is  about  0.2.  As  the  actual  density  may 
be  less  than  the  limit  by  an  indefinite  amount, 
the  general  conclusion  from  his  work  may  be  re- 
garded as  the  same  with  that  from  the  work  of 
Roberts. 

The  results  of  the  preceding  theory  are  independ- 
ent of  the  parallax  of  the  stars.  They,  therefore,  give 
us  no  knowledge  as  to  the  mass  of  a  binary  system. 
To  determine  this  we  must  know  its  parallax,  from 
which  we  can  determine  the  actual  dimensions  of  the 
orbit  when  its  apparent  dimensions  are  known.  Then 
the  formula  already  given  will  give  the  actual  mass  of 
the  system  in  terms  of  the  sun's  mass. 

There  are  only  six  binary  systems  of  which  both  the 
orbit  and  the  parallax  are  known.  These  are  shown 
in  the  table  below.  Here  the  first  two  columns  after 
the  stars  named  give  the  semi-major  axis  of  the  orbit 
and  the  measured  parallax.  The  quotient  of  the  first 
number  by  the  second  is  the  actual  mean  radius  of 
the  orbits  in  terms  of  the  earth's  distance  from  the  sun 
as  unity.  This  is  given  in  the  third  column,  after 
which  follow  the  period  and  the  resulting  combined 
mass  of  the  system.  The  last  column  shows  the 
actual  amount  of  light  emitted  by  the  system,  com- 
pared with  that  emitted  by  the  sun. 


204 


CONSTITUTION  OF  THE  STARS 


A.' 

PAR. 

A. 

PERIOD. 

MASS. 

LIGHT. 

TJ  Cassiopiae  

8.21 

O.2O 

4I.O 

IQS.8 

1.8 

I.O 

Sirius                    .  . 

8  01 

O  17 

2  1.7 

^2.2 

1.7 

12  O 

Procyon 

?  QO 

o  10 

IO  O 

40  o 

06 

8  q 

a  Centauri  

17.70 

0.75 

21.6 

81.1 

2.O 

1.7 

70  Ophiuchi    . 

A.  C  C 

O  IQ 

24  O 

884 

i  8 

o  7 

85  Pegasi  

0.89 

0.0? 

17.8 

24.0 

o.o 

2.2 

Even  in  these  few  cases  some  of  the  numbers  on 
which  the  result  depends  are  extremely  uncertain.  In 
the  case  of  Procyon,  the  radius  of  the  orbit  can  be 
only  a  rough  estimate.  In  the  case  of  85  Pegasi  the 
parallax  is  uncertain.  In  the  case  of  Eta  Cassiopiae 
the  elements  are  still  doubtful. 

So  far  as  we  have  set  forth  the  principles  involved 
in  the  question,  we  do  not  get  separate  results  for  the 
mass  of  each  body.  The  latter  can  be  determined 
only  by  meridian  observations,  showing  the  motion 
of  the  brighter  star  around  the  common  centre  of 
gravity  of  the  two.  This  result  has  thus  far  been 
worked  out  with  an  approximation  to  exactness  only 
in  the  cases  of  Sirius  and  Procyon.  For  these  systems 
we  have  the  following  masses  of  the  companions  of 
these  bodies  in  terms  of  the  sun's  mass : 


Companion  of  Sirius. . . 
Companion  of  Procyon 


1.2 

0.2 


It  will  now  be  interesting  to  compare  the  bright- 
ness of  these  bodies  with  that  which  the  sun  would 
have  if  seen  at  their  distance.  In  a  former  chapter  we 
showed  how  this  could  be  done.  The  results  are  : 


MASSES  AND  DENSITIES  OF  THE  STARS  205 

At  the  distance  of  Procyon  the  apparent  magni- 
tude of  the  sun  would  be  2m.8.  At  the  distance  of 
Sirius,  it  would  be  2m.3.  Supposing  the  sun  to  be 
changed  in  size,  its  density  remaining  unchanged, 
until  it  had  the  same  mass  as  the  respective  com- 
panions of  Procyon  and  Sirius,  its  magnitudes  would 
be: 

For  companion  of  Procyon 3.9 

For  companion  of  Sirius 2.9 

These  numbers  are  the  magnitudes  the  compan- 
ions would  show  were  they  models  of  our  sun.  Their 
actual  magnitudes  cannot  be  estimated  with  great 
precision,  owing  to  the  effect  of  the  brilliancy  of  the 
star.  From  the  estimate  of  the  companion  of  Sirius, 
by  Professor  Pickering,  its  magnitude  was  about  the 
eighth.  It  is  probable  that  the  magnitude  of  the 
companion  of  Procyon  is  not  very  different.  It  will 
be  seen  that  these  magnitudes  are  very  different  from 
those  which  they  would  have  were  they  models  of  the 
sun.  What  is  very  curious  is  that  they  differ  in  the 
opposite  direction  from  the  stars  in  general,  and 
especially  from  their  primaries.  Either  they  have  a 
far  less  surface  brilliancy  than  the  sun  or  their  density 
is  much  greater.  There  can  be  no  doubt  that  the 
former  rather  than  the  latter  is  the  case. 

This  great  mass  of  the  two  companions  as  colm- 
pared  with  their  brilliancy  suggests  the  question 
whether  they  may  not  shine,  in  part  at  least,  by  the 
light  of  their  primaries.  A  very  little  consideration 
will  show  that  this  cannot  be  the  case.  To  shine  as 


206  CONSTITUTION  OF  THE  STARS 

brightly  as  it  does  by  reflected  light,  the  diameter  of 
the  companion  of  Sirius  would  have  to  be  enormous, 
at  least  one-thirtieth  its  distance  from  Sirius.  More- 
over, its  apparent  brightness  would  vary  so  widely 
in  different  parts  of  its  orbit  that  we  should  see  it 
almost  as  well  when  near  Sirius  as  when  distant  from 
it.  The  most  likely  cause  of  the  great  dimness  is 
the  low  temperature  of  the  bodies. 

All  these  results  point  to  the  conclusion  that  the 

stars,  or  at  least  the  brighter  among  them,  are  masses 

of  gas,  enormously  compressed  in  their  in- 

Constitu-     teri°r  by  the  gravitation  of  their  outer  parts. 

tion  of  the    We  have  now  to  show  how  this  result  was 

arrived  at,   at  least  in  the  case  of  the  sun, 

from  different  considerations,  before  the  spectroscope 

had  taught  us  anything  of  the  constitution  of  these 

bodies. 

We  must  accept,  as  one  of  the  obvious  conclusions 
of  modern  science,  the  fact  that  the  sun  and  stars 
have,  for  untold  millions  of  years,  been  radiating  heat 
into  space.  We  refrain  from  considering  the  basis  on 
which  this  conclusion  rests,  not  so  much  because  it 
must  be  considered  unquestionable,  as  because  the 
discussion  would  be  too  long  and  complex  for  the 
present  work. 

One  of  the  great  problems  of  modern  science  has 
been  to  ascertain  the  source  of  this  heat.  Before 
the  theory  of  energy  was  developed  this  problem 
suggested  no  difficulty.  In  the  time  of  Newton,  Kant 
and  even  of  La  Place  and  Herschel,  no  reason  was 
known  why  the  stars  should  not  shine  forever  without 


GASEOUS  CONSTITUTION  OF  THE  STARS   207 

change.  Now  we  know  that  when  a  body  radiates 
heat,  that  heat  is  really  an  entity  termed  energy,  of 
which  the  supply  is  necessarily  limited.  Kelvin  com- 
pared the  case  of  a  star  radiating  heat  to  that  of  a 
ship  of  war  belching  forth  shells  from  her  batteries. 
We  know  that  if  the  firing  is  kept  up,  the  supply  of 
ammunition  must  at  some  time  be  exhausted.  Have 
we  any  means  of  determining  how  long  the  store  of 
energy  in  sun  or  star  will  suffice  for  its  radiation  ? 

We  know  that  the  substances  which  mainly  com- 
pose the  sun  and  stars  are  similar  to  those  which 
compose  our  earth.  We  know  the  capacity  for  heat 
of  these  substances,  and  we  also  have  determined  how 
much  heat  the  sun  radiates  annually.  From  these 
data,  it  is  found  by  a  simple  calculation  that  the 
temperature  of  the  sun  would  be  lowered  annually  by 
more  than  two  degrees  Fahrenheit,  if  its  capacity  for 
heat  were  the  same  as  that  of  water.  If  this  capacity 
were  only  that  of  the  substances  which  compose  the 
great  body  of  the  earth,  the  lowering  of  temperature 
would  be  from  5°  to  10°  annually.  Evidently,  there- 
fore, the  actual  heat  of  the  sun  would  only  suffice  for 
a  few  thousand  years'  radiation,  if  not  in  some  way  re- 
plenished. 

When  the  difficulty  was  first  attacked,  it  was  sup- 
posed that  the  supply  might  be  kept  up  by  meteors 
falling  into  the  sun.  We  know  that  in  the  region 
round  the  sun,  and,  in  fact,  in  the  whole  solar 
system,  are  countless  minute  meteors,  some  of  which 
may  from  time  to  time  strike  the  sun.  The  amount 
of  heat  that  would  be  produced  by  the  loss  of  energy 


208  CONSTITUTION  OF  THE  STARS 

suffered  by  a  meteor  moving  many  hundred  miles  a 
second  would  be  enormously  greater  than  that  which 
would  be  produced  by  combustion.  But  critical  ex- 
amination shows  that  this  theory  cannot  have  any 
possible  basis.  Apart  from  the  fact  that  it  could  at 
best  be  only  a  temporary  device,  there  seems  to  be  no 
possibility  that  meteors  sufficient  in  mass  can  move 
round  the  sun  or  fall  into  it.  Shooting  stars  show  that 
our  earth  encounters  millions  of  little  meteors  every 
day  ;  but  the  heat  produced  by  the  collisions  is  ab- 
solutely insignificant. 

It  was  then  shown  by  Kelvin  and  Helmholtz  that 
the  sun  might  radiate  the  present  amount  of  heat  for 
several  millions  of  years  simply  from  the  fund  of 
energy  collected  by  the  contraction  of  its  volume 
through  the  mutual  gravitation  of  its  parts.  As  the  sun 
cools  it  contracts  ;  the  fall  of  its  substance  toward  the 
centre,  produced  by  this  contraction,  generates  energy, 
which  energy  is  constantly  turned  into  heat.  The 
amount  of  contraction  necessary  to  keep  up  the 
present  supply  maybe  roughly  computed  ;  it  amounts 
in  round  numbers  to  220  feet  a  year,  or  four  miles  in 
a  century. 

Accepting  this  view,  it  will  almost  necessarily  fol- 
low that  the  great  body  of  the  sun  must  be  of  gaseous 
constitution.  Were  it  solid,  its  surface  would  rapidly 
cool  off,  since  the  heat  radiated  would  have  to  be  con- 
ducted from  the  interior.  Then,  the  loss  of  heat  no 
longer  going  on  at  the  same  rate,  the  contraction  also 
would  stop  and  the  generation  of  heat  to  supply  the 
radiation  would  cease.  Even  were  the  sun  a  liquid, 


GASEOUS  CONSTITUTION  OF  THE  STARS  200 

currents  of  liquid  matter  could  scarcely  convey  to  the 
surface  a  sufficient  amount  of  heated  matter  to  supply 
the  enormous  radiation.  Thus  the  reason  of  the  case 
combines  with  observation  of  the  density  of  the  sun 
to  show  that  its  interior  must  be  regarded  as  gaseous 
rather  than  solid  or  liquid. 

A  difficult  matter,  however,  presents  itself.  The 
density  of  the  sun  is  greater  than  we  ordinarily  see  in 
gases,  being,  as  we  have  remarked,  even  greater  than 
the  density  of  water.  The  explanation  of  this 
difficulty  is  very  simple  :  the  gaseous  interior  is  sub- 
ject to  compression  by  its  superficial  portions.  The 
gravitation  on  the  surface  being  twenty-seven 
times  what  it  is  on  the  earth,  the  pressure  increases 
twenty-seven  times  as  fast  when  we  go  towards  the 
centre  as  it  does  on  the  earth.  We  should  not  have 
to  go  very  far  within  its  body  to  find  a  pressure  of 
millions  of  tons  on  the  square  inch.  Under  such 
pressure  and  at  such  an  enormous  temperature 
as  must  there  prevail,  the  distinction  between  a  gas 
and  a  liquid  is  lost  ;  the  substance  retains  the 
elasticity  of  a  gas,  while  assuming  the  density  of  a 
liquid. 

It  does  not  follow,  however,  that  the  visible  surface 
of  the  sun  is  a  gas,  pure  and  simple.  The  sudden 
cooling  which  a  mass  of  gaseous  matter  undergoes  on 
reaching  the  surface  may  liquefy  it  or  even  change  it 
into  a  solid.  But,  in  either  case,  the  sudden  contrac- 
tion which  it  thus  undergoes  makes  it  heavier  and  it 
sinks  down  again  to  be  remelted  in  the  great  furnace 
below.  It  may  well  be,  therefore,  that  the  description 


2io  CONSTITUTION  OF  THE  STARS 

of  the  sun  as  a  vast  bubble  is  nearly  true.  It  maybe 
added  .that  all  we  have  said  about  the  sun  may  very 
well  be  supposed  true  of  the  stars.  We  have  now  to 
consider  the  law  of  change  as  a  sun  or  star  contracts 
through  the  loss  of  heat  suffered  by  its  radiation  into 
space. 

This  subject  was  very  exhaustively  developed  by 
Ritter  some  years  since.1  It  is  not  practicable  to  give 
even  an  abstract  of  Ritter's  results  in  the  present  work, 
especially  as  every  mathematical  investigation  of  the 
subject  must  either  rest  on  hypotheses  more  or  less 
uncertain,  or  must,  for  its  application,  require  data 
impossible  to  obtain.  We  shall,  therefore,  confine  our- 
selves to  a  brief  outline  of  the  main  points  of  the  sub- 
ject. A  fundamental  proposition  of  the  whole  theory 
is  Lane's  law  of  gaseous  attraction,  which  is  as  follows  : 

When  a  spherical  mass  of  incandescent  gas  contracts 
throiigh  the  loss  of  its  heat  by  radiation  into  space,  its 
temperature  continually  becomes  higher  as  long  as  the 
gaseous  condition  is  retained. 

The  demonstration  of  this  law  is  simple  enough  to 
be  understood  by  anyone  well  acquainted  with  ele- 
mentary mechanics  and  physics,  and  it  will  also  fur- 
nish the  basis  for  our  consideration  of  the  subject. 

We  begin  by  some  considerations  on  the  condition 
of  a  mass  of  gas  held  together  by  the  mutual  at- 
traction of  its  parts.  This  attraction  results  in  a 
certain  hydrostatic  pressure,  capable  of  being  ex- 
pressed as  so  many  pounds  or  tons  per  unit  of  sur- 
face, say  a  square  inch.  This  pressure  at  any  point 

1  Wiedemann's  Annalen  der  Physik  n.  Chemie,  1878  to  1883,  etc. 


INCREASING  TEMPERATURE  OF  THE  STARS  211 

is  equal  to  the  weight  of  a  column  of  the  gas  having 
a  section  of  one  square  inch  and  extending  from  the 
point  in  question  to  the  surface.  It  is  a  law  of  at- 
traction, in  a  sphere  of  which  the  density  is  the  same 
at  equal  distances  from  its  centre,  that  if  we  suppose 
an  interior  sphere  concentric  with  the  body,  the  at- 
traction, of  all  the  matter  outside  that  interior  sphere, 
on  any  point  within  it,  is  equal  in  every  direction, 
and,  therefore,  is  completely  neutralised.  A  point  is, 
therefore,  drawn  towards  the  centre  only  by  the 
attraction  of  matter  inside  the  sphere  on  the  surface 
of  which  it  lies. 

At  every  point  in  the  interior  the  hydrostatic  pres- 
sure must  be  balanced  by  the  elastic  force  of  the  gas. 
In  the  case  of  any  one  gas  this  force  is  proportional 
to  the  product  of  the  density  into  the  absolute  tern 
perature.  This' condition  of  equilibrium  must  be 
satisfied  at  every  point  throughout  the  mass. 


Let  the  two  circles  in  the  figure  represent  gaseous 
globes  of  the  kind  supposed.  The  larger,  A,  repre- 
sents the  globe  in  a  certain  condition  of  its  evolution  ; 
the  smaller,  B,  its  condition  after  its  volume  has 


212  CONSTITUTION  OF  THE  STARS 

contracted  to  one-half.  The  temperature  in  each 
case  will  necessarily  increase  from  the  surface  to  the 
centre.  The  law  of  this  increase  is  incapable  of 
accurate  expression,  but  is  not  necessary  for  our 
present  purpose. 

Let  the  inner  circle,  C  D,  represent  a  spherical 
shell  of  the  matter  forming  the  body,  situated  any- 
where in  the  interior  of  the  mass,  but  concentric 
with  it.  Let  E  F  be  the  corresponding  shell  after 
the  contraction  has  taken  place.  The  case  will  then 
be  as  follows  : 

The  two  shells  will  by  hypothesis  have  the  same 
quantity  of  matter,  both  in  their  own  substance  and 
throughout  their  interior. 

In  case  B,  the  central  attraction,  being  as  the  in- 
verse square  of  the  distance  from  the  centre,  will  be 
four  times  as  great  for  each  unit  of  matter  in  the 
shell. 

This  force  of  attraction,  tending  to  compress  the 
shell,  is,  in  case  B,  exerted  on  a  surface  one  quarter 
as  great,  because  the  surface  of  a  shell  is  proportional 
to  the  square  of  its  diameter. 

Hence  the  hydrostatic  pressure  per  unit  of  surface 
is  sixteen  times  as  great  in  case  B  as  in  case  A. 

The  elastic  force  of  the  gas,  if  the  two  bodies  were 
at  the  same  temperature,  would  be  eight  times  as 
great  in  case  B  as  in  case  A,  being  inversely  as  the 
volume. 

The  hydrostatic  pressure  being  sixteen  times  as 
great,  while  the  elastic  force  to  counterbalance  it  is 
only  eight  times  as  great,  no  equilibrium  would  be 


INCREASING  TEMPERATURE  OF  THE  STARS  213 

possible.  To  make  it  possible,  the  absolute  tempera- 
ture of  the  gas  must  be  doubled,  in  order  that  the 
elastic  force  shall  balance  the  pressure.  The  tem- 
perature of  the  spherical  surface  E  F  will  therefore 
be  double  that  of  the  surface  C  D. 

That  a  mass  can  become  hotter  through  cooling, 
may,  at  first  sight,  seem  paradoxical.  We  shall, 
therefore,  cite  a  result  which  is  strictly  analogous. 
If  the  motion  of  a  comet  is  hindered  by  a  resisting 
medium,  the  comet  will  continually  move  faster. 
The  reason  of  this  is  that  the  first  effect  of  the 
medium  is  to  diminish  the  velocity  of  the  object. 
Through  this  diminution  of  velocity,  the  comet  falls 
towards  the  sun.  The  increase  of  velocity  caused  by 
the  fall  more  than  counterbalances  the  diminution 
produced  by  the  resistance.  The  result  is  that  the 
comet  takes  up  a  more  and  more  rapid  motion,  as  it 
gradually  approaches  the  sun,  in  consequence  of  the 
resistance  it  suffers.  In  the  same  way,  when  a  gas- 
eous celestial  body  cools,  the  fall  of  its  mass  towards 
the  centre  changes  an  amount  of  energy  greater  than 
that  radiated  away  from  a  potential  to  an  actual 
form. 

The  critical  reader  will  see  a  weak  point  in  this 
reasoning,  which  it  is  necessary  to  consider.  What 
we  have  really  shown  is  that  if  the  mass,  being  in 
equilibrium  when  it  has  the  volume  A,  has  to  remain 
in  equilibrium  when  it  is  reduced  to  the  volume  B, 
then  its  temperature  must  be  doubled.  But  we  have 
not  proved  that  its  temperature  actually  will  be 
doubled  by  the  fall.  In  fact,  it  cannot  be  doubled 


214  CONSTITUTION  OF  THE  STARS 

unless  the  energy  generated  by  the  fall  of  the  super- 
ficial portions  towards  the  centre  is  sufficient  to 
double  the  absolute  amount  of  heat.  Whether  this 
will  be  the  case  depends  on  a  variety  of  circum- 
stances, including  the  mass  of  the  body,  and  the  capac- 
ity of  its  substance  for  heat.  If  we  are  to  proceed 
with  mathematical  rigour,  it  is,  therefore,  necessary  to 
determine  in  any  given  case  whether  this  condition  is 
fulfilled.  Let  us  suppose  that  in  any  particular  case 
the  mass  is  so  small  or  the  capacity  for  heat  so  con- 
siderable that  the  temperature  is  not  doubled  by  the 
contraction.  Then  the  contraction  will  go  on  further 
and  further,  until  the  mass  becomes  a  solid.  But 
in  this  case  let  us  reverse  the  process.  The  body 
being  supposed  nearly  in  a  state  of  equilibrium  in 
position  A,  let  the  elastic  force  be  slightly  in  excess. 
Then  the  gas  will  expand.  In  order  that  it  shall  be  re- 
duced to  a  state  of  equilibrium  by  expansion,  its  tem- 
perature must  diminish  according  to  the  same  law 
that  it  would  increase  if  it  contracted.  When  its  di- 
ameter doubles,  its  temperature  should  be  reduced  to 
one-half  or  less  by  the  expansion,  in  order  that  the 
equilibrium  shall  subsist.  But,  in  the  case  supposed, 
the  temperature  is  not  reduced  so  much  as  this. 
Hence,  it  is  too  high  for  equilibrium  by  a  still  greater 
amount  and  the  expansion  must  go  on  indefinitely. 
Thus,  in  the  case  supposed,  the  hypothetical  equili- 
brium of  the  body  is  unstable.  In  other  words,  no 
such  body  is  possible. 

This  conclusion  is  of  fundamental  importance.      It 
shows  that  the  possible  mass  of  a  star  must  have  an 


TEMPERATURES  OF  DIFFERENT  STARS    215 

inferior  limit,  depending  on  the  quantity  of  matter  it 
contains,  its  elasticity  under  given  circumstances,  and 
its  capacity  for  heat  It  is  certain  that  any  small  mass 
of  gas,  taken  into  celestial  space  and  left  to  itself, 
would  not  be  kept  together  by  the  mutual  attraction 
of  its  parts,  but  would  merely  expand  into  indefinite 
space.  Possibly  this  might  be  true  of  the  earth,  if  it 
were  gaseous.  The  computation  would  not  be  a 
difficult  one  to  make,  but  I  have  not  made  it. 

In  what  precedes,  we  have  supposed  a  single  mass 
to  contract.  But  our  study  of  the  relations  of  tem- 
perature and  pressure  in  the  two  masses  assumes  no 
relationship  between  them,  except  that  of  equality. 
Let  us  now  consider  any  two  gaseous  bodies,  A  and 
B,  and  suppose  that  the  body  B,  instead  of  having 
the  same  mass  as  A,  is  another  body  with  a  different 
mass. 

Since  the  mass  B  may  be  of  various  sizes,  according 
to  the  amount  of  contraction  it  has  undergone,  let  us 
begin  by  supposing  it  to  have  the  same  volume  as  A, 
but  twice  the  mass  of  A.  We  have  then  to  inquire 
what  must  be  its  temperature  in  order  that  it  may  be 
in  equilibrium.  We  have  first  to  inquire  into  the  hy- 
drostatic pressure  at  any  point  of  the  interior.  Refer- 
ring to  either  of  the  bodies  in  the  figure  of  p.  211, 
a  spherical  shell  like  CD  will  now,  in  the  case  of 
the  more  massive  body,  have  double  the  mass  of  the 
corresponding  shell  of  A.  The  attraction  will  also 
be  doubled,  because  the  diameter  of  the  spherical 
shell  is  the  same,  while  the  amount  of  matter  within 
it  is  twice  as  great.  Hence  the  hydrostatic  pressure 


2i6  CONSTITUTION  OF  THE  STARS 

per  unit  of  surface  will  be  four  times  as  great,  or  will 
vary  as  the  square  of  the  density.  The  elasticity  at 
equal  temperatures  being  proportional  to  the  density, 
it  follows  that,  were  the  temperature  the  same  in  the 
two  masses,  the  elasticity  would  be  double  in  the 
case  of  mass  B  ;  whereas,  to  balance  the  hydrostatic 
pressure,  it  should  be  quadrupled.  The  temperature 
of  B  must,  therefore,  be  twice  as  great  as  that  of  A. 
It  follows  that  in  the  case  of  stars  of  equal  volume, 
but  of  different  masses,  the  temperature  must  be  pro- 
portional to  the  mass  or  density. 

But  how  will  it  be  if  we  suppose  the  density  of  the 
two  bodies  to  be  the  same,  and,  therefore,  the  mass 
to  be  proportional  to  the  volume?  In  this  case  the 
attraction  at  a  given  point  will  be  proportional  to  the 
diameter  of  the  body.  If,  then,  we  suppose  one  body 
to  have  twice  the  diameter  of  the  other,  but  to  be  of 
the  same  density,  it  follows  that  at  corresponding 
points  of  the  interior,  the  hydrostatic  pressure  will  be 
twice  as  great  in  the  larger  body.  The  density  being 
the  same,  it  follows  that  the  temperature  must  be 
twice  as  high  in  order  that  equilibrium  may  be  main- 
tained. It  follows  that  the  stars  of  the  greatest  mass 
will  be  at  the  highest  temperature,  unless  their  volume 
is  so  great  that  their  density  is  less  than  that  of  the 
smaller  stars. 


CHAPTER  XIII 
STELLAR  EVOLUTION 

As  yet  this  world  was  not,  and  Chaos  wild 

Reigned  where  these  heavens  now  roll,  where  earth  now  rests. 

MILTON, 

Und  Sturme  brausen  um  die  Wette 
Vom  Meer  aufs  Land  vom  Land  aufs  Meer 
Und  bilden  wiithend  eine  Kette 
Der  tiefsten  Wirkung  ringsumher. 

GOETHE. 

IT  follows  from  the  theory  set  forth  in  the  last 
chapter  that  the  stars  are  not  of  fixed  constitu- 
tion, but  are  all  going  through  a  progressive  change 
— cooling  off  and  contracting  into  a  smaller  volume. 
If  we  accept  this  result,  we  find  ourselves  face  to  face 
with  an  unsolvable  enigma, — How  did  the  evolution  of 
the  stars  begin  ?  To  show  the  principle  involved  in 
the  question,  I  shall  make  use  of  an  illustration  drawn 
from  another  work.  An  inquiring  person,  wandering 
around  in  what  he  supposes  to  be  a  deserted  building, 
finds  a  clock  running.  If  he  knows  nothing  about 
the  construction  of  the  clock,  or  the  force  necessary 
to  keep  it  in  motion,  he  may  fancy  that  it  has  been 
running  for  an  indefinite  time  just  as  he  sees  it,  and 
that  it  will  continue  to  run  until  the  material  of  which 
217 


2i8  STELLAR  EVOLUTION 

it  is  made  shall  wear  out.  But  if  he  is  acquainted 
with  the  laws  of  mechanics,  he  will  know  that  this  is 
impossible,  because  the  continued  movement  of  the 
pendulum  involves  a  constant  expenditure  of  energy. 
If  he  studies  the  construction  of  the  clock,  he  will 
find  the  source  of  this  energy  in  the  slow  falling  of  a 
weight  suspended  by  a  cord  which  acts  upon  a  train  of 
wheels.  Watching  the  motions,  he  will  see  that  the 
scape-wheel  acting  on  the  pendulum  moves  very  per- 
ceptibly every  second,  while  he  must  watch  the  next 
wheel  Tor  several  seconds  to  see  any  motion.  If  the 
time  at  his  disposal  is  limited,  he  will  not  be  able  to 
see  any  motion  at  all  in  the  weight.  But  an  examina- 
tion of  the  machinery  will  show  him  that  the  weight 
must  be  falling  at  a  certain  rate,  and  he  can  compute 
that  at  the  end  of  a  certain  time  the  weight  will  reach 
the  bottom,  and  the  clock  will  stop.  He  can  also  see 
that  there  must  have  been  a  point  from  above  which 
the  weight  could  never  have  fallen.  Knowing  the 
rate  of  fall,  he  can  compute  how  long  the  weight  occu- 
pied in  falling  from  this  point.  His  final  conclusion 
will  be  that  the  clock  must  in  some  way  have  been 
wound  up  and  set  in  motion  by  an  external  force  a 
certain  number  of  hours  or  days  before  his  inspection, 
and  must  be  again  wound  up  by  such  a  force  unless  it 
is  to  stop. 

If  we  accept  the  theory  that  the  heat  of  the  stars  is 
kept  up  by  their  slow  contraction  we  must  think  of  the 
universe  of  stars  as  of  a  clock  which  is  running  down. 
As  we  can  see  by  the  eye  of  reason  that  the  weight  of 
the  clock  was  higher  yesterday  than  it  is  to-day,  so  we 


STELLAR  EVOLUTION 


219 


can  compute  that  the  stars  must  have  been  larger  in 
former  times,  and  that  there  must  have  been  some 
finite  and  computable  period  when  they  were  all 
nebulae.  Not  even  a  nebula  can  give  light  without  a 
progressive  change  of  some  sort.  Hence,  within  a  cer- 
tain finite  period  the  nebulae  themselves  must  have  be- 
gun to  shine.  How  did  they  begin  ?  This  is  the  un- 
solvable  question. 

The  process  of  stellar  evolution  may  be  discussed 
without  considering  this  question.  Accepting  as  a 
fact,  or  at  least  as  a  working  hypothesis,  that  the  stars 
are  contracting,  we  find  a  remarkable  consistency  in 
the  results.  Year  by  year  laws  are  established  and 
more  definite  conclusions  reached.  It  is  now  possible 
to  speak  of  the  respective  ages  of  stars  as  they  go 
through  their  progressive  course  of  changes.  This 
subject  has  been  so  profoundly  studied  and  so  fully 
developed  by  Sir  William  and  Lady  Huggins  that  I 
shall  depend  largely  on  their  work  in  briefly  setting  it 
forth.1  At  the  same  time,  in  an  attempt  to  condense 
the  substance  of  many  folio  pages  into  so  short  a  space, 
one  can  hardly  hope  to  be  entirely  successful  in  giving 
merely  the  views  of  the  original  author.  The  follow- 
ing may,  therefore,  be  regarded  as  partly  the  views  of 
Sir  William  Huggins,  condensed  and  arranged  in  the 
order  in  which  they  present  themselves  to  the  writer's 
mind,  and  partly  those  of  the  writer  himself. 

There  is  an  infinite  diversity  among  the  spectra  of 
the  stars  ;  scarcely  two  are  exactly  alike  in  all  their  de- 
tails. But  the  larger  number  of  these  spectra,  when 

1  Publications  of  Sir  William   Huggins's  Observatory,  vol.  i.,  London,  1899. 


220  STELLAR  EVOLUTION 

carefully  compared,  may  be  made  to  fall  in  line,  thus 
forming  a  series  in  which  the  passage  of  one  spectrum 
into  the  next  in  order  is  so  gradual  as  to  indicate  that 
the  actual  differences  represent,  in  the  main,  successive 
epochs  of  star  life  rather  than  so  many  fundamental 
differences  of  chemical  constitution.  Each  star  may 
be  considered  to  go  through  a  series  of  changes  an- 
alogous to  those  of  a  human  being  from  birth  to  old 
age.  In  its  infancy  a  star  is  simply  a  nebulous  mass  ; 
it  gradually  condenses  into  a  smaller  volume,  growing 
hotter,  as  set  forth  in  the  last  chapter,  until  a  stage  of 
maximum  temperature  is  reached,  when  it  begins  to 
cool  off.  Of  the  duration  of  its  life  we  cannot  form 
an  accurate  estimate.  We  can  only  say  that  it  is  cer- 
tainly to  be  reckoned  by  millions  and  probably  by  tens 
of  millions  or  even  hundreds  of  millions  of  years.  We 
thus  have  in  the  heavens  stars  ranging  through  the 
whole  series  from  the  earliest  infancy  to  old  age. 
How  shall  we  distinguish  the  order  of  development  ? 
Mainly  by  their  colours  and  their  spectra.  In  its  first 
stage  the  star  is  of  a  bluish  white.  It  gradually  passes 
through  white  into  yellow  and  red.  Sir  William  gives 
the  following  series  of  stars  as  an  example  of  the  suc- 
cessive stages  of  development : 

Sirius  ;  a  Lyrae. 
a  Ursae  Majoris. 
a  Virginis. 
a  Aqtiilas. 
Rigel. 
of  Cygni. 

Capella  ;  the  sun. 


LIFE  HISTORY  OF  A  STAR  221 

Arcturus. 
Aldebaran. 
a  Orionis. 

The  length  of  the  life  of  a  star  has  no  fixed  limit ;  it 
depends  entirely  on  the  mass.  The  larger  the  mass, 
the  longer  the  life  ;  hence  a  small  star  may  pass  from 
infancy  to  old  age  many  times  more  rapidly  than  a 
large  one. 

At  the  same  time,  up  to  at  least  the  yellow  stage, 
the  star  continually  grows  hotter  as  it  condenses.  A 
difficulty  may  here  suggest  itself  in  reconciling  this 
order  with  a  well-known  physical  fact.  As  a  radiating 
body  increases  in  temperature,  its  color  changes  from 
red  through  yellow  to  white,  and  the  average  wave- 
length of  its  light  continually  diminishes.  We  see  a 
familiar  example  of  this  in  the  case  of  iron,  which 
when  heated  is  first  red  in  color  and  then  goes 
through  the  changes  we  have  mentioned.  The  ordi- 
nary incandescent  electric  light  is  yellow,  the  arc  light, 
the  most  intense  that  we  can  produce  by  artificial 
means,  is  white.  When  the  spectrum  of  a  body  thus 
increasing  in  temperature  is  watched,  the  limit  is  found 
to  pass  gradually  from  the  red  toward  the  violet  end. 
It  would  seem,  therefore,  that  the  hotter  stars  should 
be  the  white  ones  and  the  cooler  the  yellow  or  red 
ones. 

There  are,  however,  two  circumstances  to  be  ^con- 
sidered in  connection  with  the  contracting  star.  In  the 
first  place,  the  light  which  we  receive  from  a  star  does 
not  emanate  from  its  hottest  interior,  but  from  a  re- 
gion either  upon  or,  in  most  cases,  near  its  surface.  It 


222  STELLAR  EVOLUTION 

is,  therefore,  the  temperature  of  this  region  which  de- 
termines the  colour  of  the  light.  In  the  next  place, 
part  of  the  light  is  absorbed  by  passing  through  the 
cooler  atmosphere  surrounding  the  star.  It  is  only 
the  light  which  escapes  through  this  atmosphere  that 
we  actually  see. 

In  the  case  of  the  sun  all  the  light  which  it  sends 
forth  comes  from  a  comparatively  shallow  bounding 
layer,  the  photosphere.  The  most  careful  telescopic 
examination  shows  no  depth  to  this  layer,  which 
would  rapidly  cool  off  were  it  not  for  convection  cur- 
rents bringing  up  heated  matter  from  the  interior. 
It  might  be  supposed  that  such  a  current  would  result 
in  the  surface  being  kept  at  nearly  as  high  a  tempera- 
ture as  the  interior ;  but,  as  a  matter  of  fact,  the 
opposite  is  the  case.  As  the  volume  of  gas  rises,  it 
expands  from  the  diminished  pressure  and  it  is  thus 
cooled  in  the  very  act  of  coming  to  the  surface,  as 
well  as  by  the  rapid  radiation  when  it  reaches  the 
surface. 

In  the  case  of  younger  stars,  there  is  probably  no 
photosphere,  properly  so  called.  The  light  which 
they  emit  comes  from  a  considerable  distance  in  the 
interior.  Here  the  effect  of  gravity  comes  into  play. 
The  more  the  star  condenses,  the  greater  is  gravity  at 
its  surface ;  hence  the  more  rapidly  does  the  density 
of  the  gas  increase  from  the  surface  toward  the  in- 
terior. In  the  case  of  the  sun,  the  density  of  any 
gas  which  may  immediately  surround  the  photosphere 
must  be  doubled  every  mile  or  two  of  its  depth  until 
we  reach  the  photosphere.  But  if  the  sun  were  many 


LIFE  HISTORY  OF  A  STAR  223 

times  its  present  diameter,  this  increase  would  be 
very  much  slower.  Hence,  when  the  volume  is  very 
great  the  increase  of  density  is  comparatively  slow  ; 
there  being  no  well-defined  photosphere,  the  light 
reaches  us  from  a  much  greater  depth  from  the  in- 
terior than  it  does  at  a  later  stage. 

The  gradual  passing  of  a  white  star  into  one  of  the 
solar  type  is  marked  by  alterations  in  its  spectrum. 
These  alterations  are  especially  seen  in  the  behaviour 
of  the  lines  of  hydrogen,  calcium,  magnesium,  and 
iron.  The  lines  of  hydrogen  change  from  broad  to 
thin  ;  those  of  calcium  constantly  become  stronger. 

Of  the  greatest  interest  is  the  question,  At  what 
stage  does  the  temperature  of  the  star  reach  its  maxi- 
mum and  the  body  begin  to  cool  ?  Has  our  sun 
reached  this  stage  ?  This  is  a  question  to  which, 
owing  to  the  complexity  of  the  conditions,  it  is  im- 
possible to  give  a  precise  answer.  It  seems  probable, 
however,  that  the  highest  temperature  is  reached  in 
about  the  stage  of  our  sun.  Accepting  Sir  William 
Huggins's  view,  the  reason  the  light  is  not  then  bluest 
is  that  it  suffers  a  strong  selective  absorption  by  the 
gases  surrounding  the  photosphere.  We  know  this 
to  be  the  case  with  the  sun.  According  to  Vogel,  the 
removal  of  the  sun's  atmosphere  would  make  its 
light  two-and-a-half  times  as  bright  at  the  blue-violet 
end  of  the  spectrum. 

The  general  fact  that  every  star  has  a  life  history 
— that  this  history  will  ultimately  come  to  an  end— 
that  it  must  have  had  a  beginning  in  time — is  indi- 
cated by  so  great  a  number  of  concurring  facts  that 


224  STELLAR  EVOLUTION 

no  one  who  has  most  profoundly  studied  the  subject 
can  have  serious  doubts  upon  it.  Yet  there  are  some 
unsolved  mysteries  connected  with  the  case,  which 
might  justify  a  waiting  for  further  evidence,  coupled 
with  a  certain  degree  of  scepticism.  Of  the  questions 
connected  with  the  case  the  most  serious  one  is  raised 
by  the  geologists. 

On  the  theory  set  forth  in  the  last  chapter,  that 
the  radiant  energy  sent  out  is  balanced  by  the  con- 
tinual loss  of  potential  energy  due  to  the  contraction, 
the  age  of  the  sun  can  be  at  least  approximately  esti- 
mated. About  twenty  millions  of  years  is  the  limit 
of  time  during  which  it  could  possibly  have  radiated 
anything  like  its  present  amount  of  energy.  But  this 
conclusion  is  directly  at  variance  with  that  of  geology. 
The  age  of  the  earth  has  been  approximately  esti- 
mated from  a  great  variety  of  geological  phenomena, 
the  concurring  result  being  that  stratification  and 
other  geological  processes  must  have  been  going  on 
for  hundreds — nay,  thousands  of  millions  of  years. 
This  result  is  in  direct  conflict  with  the  only  physical 
theory  which  can  account  for  the  solar  heat. 

The  nebulae  offer  a  similar  difficulty.  Their  ex- 
treme tenuity  and  their  seemingly  almost  immaterial 
structure  appear  inadequate  to  account  for  any  such 
mutual  gravitation  of  their  parts  as  would  result  in 
the  generation  of  the  fiood  of  energy  which  they  are 
constantly  radiating.  What  we  see  must,  therefore, 
suggest  at  least  the  possibility  that  all  shining  heav- 
enly bodies  have  connected  with  them  some  source 
of  energy  of  which  science  can,  as  yet,  render  no 


STELLAR  EVOLUTION  225 

account.  Facts  are  accumulating  which  converge  to 
the  view  that  forms  of  substance  exist  which  are 
neither  matter  nor  ether,  but  something  between  the 
two — perhaps  primeval  substance  from  which  matter 
itself  was  evolved.  In  this  ethereal  substance  is  stored 
an  almost  exhaustless  supply  of  energy,  the  with- 
drawal of  which  results  in  the  condensation  of  the 
substance  into  matter.  More  than  this  it  seems  hard 
to  say  until  we  have  either  seen  the  nebulae  contract- 
ing in  volume,  or  have  made  such  estimates  of  their 
probable  masses  that  we  can  compute  the  amount  of 
contraction  they  must  undergo  to  maintain  the  supply 
of  energy. 


CHAPTER  XIV 

THE  STRUCTURE  OF  THE  HEAVENS 

He  who  through  vast  immensity  can  pierce, 

See  worlds  on  worlds  compose  one  universe, 

Observe  how  system  into  system  runs, 

What  other  planets  circle  other  suns, 

What  varied  being  peoples  every  star, 

May  tell  why  Heaven  has  made  us  as  we  are. —  POPE. 

THE  problem  of  the  structure  and  duration  of  the 
universe  is  the  most  far-reaching  with  which  the 
mind  has  to  deal.  Its  solution  may  be  regarded  as 
the  ultimate  object  of  stellar  astronomy,  the  possibil- 
bility  of  reaching  which  has  occupied  the  minds  of 
thinkers  since  the  beginning  of  civilisation.  Before 
our  time  the  problem  could  be  considered  only  from 
the  imaginative  or  the  speculative  point  of  view. 
Although  we  can  to-day  attack  it  to  a  limited  extent 
by  scientific  methods,  it  must  be  admitted  that  we 
have  scarcely  taken  more  than  the  first  step  toward 
the  actual  solution.  We  can  do  little  more  than 
state  the  questions  involved,  and  show  what  light,  if 
any,  science  is  able  to  throw  upon  the  possible 
answers. 

First,  we    may   inquire   as    to    the    extent    of   the 
universe  of  stars.     Are  the  latter  scattered  through 
226 


SS  THE  UNIVERSE  INFINITE!  227 

infinite  space,  so  that  those  we  see  are  merely  that 
portion  of  an  infinite  collection  which  happens  to  be 
within  reach  of  our  telescopes,  or  are  all  the  stars 
contained  within  a  certain  limited  space  ?  In  the 
latter  case,  have  our  telescopes  yet  penetrated  to  the 
boundary  in  any  direction  ?  In  other  words,  as,  by 
the  aid  of  increasing  telescopic  power,  we  see  fainter 
and  fainter  stars,  are  these  fainter  stars  at  greater 
distances  than  those  before  known,  or  are  they  smal- 
ler stars  contained  within  the  same  limits  as  those  we 
already  know  ?  Otherwise  stated,  do  we  see  stars 
on  the  boundary  of  the  universe  ? 

Secondly,  granting  the  universe  to  be  finite,  what 
is  the  arrangement  of  the  stars  in  space  ?  Especially, 
what  is  the  relation  of  the  galaxy  to  the  other  stars  ? 
In  what  sense,  if  any,  can  the  stars  be  said  to  form  a 
permanent  system  ?  Do  the  stars  which  form  the 
Milky  Way  belong  to  a  different  system  from  the 
other  stars,  or  are  the  latter  a  part  of  one  universal 
system  ? 

Thirdly,  what  is  the  duration  of  the  universe  in 
time  ?  Is  it  fitted  to  last  for  ever  in  its  present  form, 
or  does  it  contain  within  itself  the  seeds  of  dissolu- 
tion ?  Must  it,  in  the  course  of  time,  in  we  know 
not  how  many  millions  of  ages,  be  transformed  into 
something  very  different  from  what  it  now  is  ?  This 
question  is  intimately  associated  with  the  question 
whether  the  stars  form  a  system.  If  they  do,  we 
may  suppose  that  system  to  be  permanent  in  its 
general  features  ;  if  not,  we  must  look  further  for  our 
conclusion. 


22S  STRUC  TURE  O  F  THE  HEA  VENS  . 

The  first  and  third  of  these  questions  will  be 
recognised  by  students  of  Kant  as  substantially  those 
raised  by  the  great  philosopher  in  the  form  of  anti- 
nomies. Kant  attempted  to  show  that  both  the 
propositions  and  their  opposites  could  be  proved  or 
disproved  by  reasoning  equally  valid  in  either  case. 
The  doctrine  that  the  universe  is  infinite  in  duration 
and  that  it  is  finite  in  duration  are  both,  according  to 
him,  equally  susceptible  of  disproof.  To  his  reason- 
ing on  both  points  the  scientific  philosopher  of  to- 
day will  object  that  it  seeks  to  prove  or  disprove,  a 
priori,  propositions  which  are  matters  of  fact,  of 
which  the  truth  can  be  therefore  settled  only  by  an 
appeal  to  observation.  The  more  correct  view  is 
that  afterward  set  forth  by  Sir  William  Hamilton, 
that  it  is  equally  impossible  for  us  to  conceive  of  in- 
finite space  (or  time),  or  of  space  (or  time)  coming  to 
an  end.  But  this  inability  merely  grows  out  of  the 
limitations  of  our  mental  power,  and  gives  us  no  clue 
to  the  actual  universe.  So  far  as  the  questions  are 
concerned  with  the  latter,  no  answer  is  valid  unless 
based  on  careful  observation.  Our  reasoning  must 
have  facts  to  start  from  before  a  valid  conclusion  can 
be  reached. 

The  first  question  we  have  to  attack  is  that  of  the 
extent  of  the  universe.  In  its  immediate  and  practi- 
cal form,  it  is  whether  the  smallest  stars  that  we  see 
are  at  the  boundary  of  a  system,  or  whether  more 
and  more  lie  beyond  to  an  infinite  extent.  This 
question  we  are  not  yet  ready  to  answer  with  any 
approach  to  certainty.  Indeed,  from  the  very  nature 


JS  THE  UNI  VERSE  INFINI TE?  229 

of  the  case,  the  answer  must  remain  somewhat  in- 
definite. If  the  collection  of  stars  which  forms  the 
Milky  Way  be  really  finite,  we  may  not  yet  be  able 
to  see  its  limit.  If  we  do  see  its  limit,  there  may  yet 
be,  for  aught  we  know,  other  systems  and  other 
galaxies,  scattered  through  infinite  space,  which  must 
for  ever  elude  our  powers  of  vision.  Quite  likely  the 
boundary  of  the  system  may  be  somewhat  indefinite, 
the  stars  gradually  thinning  out  as  we  go  farther  and 
farther,  so  that  no  definite  limit  can  be  assigned.  If 
all  stars  are  of  the  same  average  brightness  as  those 
we  see,  all  that  lie  beyond  a  certain  distance  must 
evade  observation,  at  least  as  individual  stars,  for  the 
simple  reason  that  they  are  too  far  off  to  be  visible 
in  our  telescopes. 

There  is  a  law  of  optics  which  throws  some  light 
on  the  question.  Suppose  the  stars  to  be  scattered 
through  infinite  space  in  such  a  way  that  every  great 
portion  of  space  is,  in  the  general  average,  about 
equally  rich  in  stars.  Then  imagine  that,  at  some 
great  distance,  say  that  of  the  average  stars  of  the 
sixth  magnitude,  we  describe  a  sphere  having  its 
centre  in  our  system.  Outside  this  sphere,  describe 
another  one,  having  a  radius  greater  by  a  certain 
quantity,  which  we  may  call  S.  Outside  that  let  there 
be  another  of  a  radius  yet  greater  by  S,  and  so  on 
indefinitely.  Thus  we  shall  have  an  endless  succes- 
sion of  concentric  spherical  shells,  each  of  the  same 
thickness,  S.  The  volume  of  each  of  these  regions 
will  be  nearly  proportional  to  the  square  of  the  diame- 
ters of  the  spheres  which  bound  it.  Hence,  supposing 


23o  STRUCTURE  OF  THE  HEAVENS 

an  equal  distribution  of  the  stars,  each  of  the 
regions  will  contain  a  number  of  stars  increasing  as 
the  square  of  the  radius  of  the  region.  Since  the 
amount  of  light  which  we  receive  from  each  individ- 
ual star  is  as  the  inverse  square  of  its  distance,  it 
follows  that  the  sum-total  of  the  light  received  from 
each  of  these  spherical  shells  will  be  equal.  Thus, 
as  we  include  sphere  after  sphere,  we  add  equal 
amounts  of  light  without  limit.  The  result  of  the  suc- 
cessive addition  of  these  equal  quantities,  increasing 
without  limit,  would  be  that  if  the  system  of  stars 
extended  out  indefinitely  the  whole  heavens  would 
be  filled  with  a  blaze  of  light  as  bright  as  the  sun. 

Now,  as  a  matter  of  fact,  such  is  very  far  from 
being  the  case.  It  follows  that  infinite  space  is  not 
occupied  by  the  stars.  At  best  there  can  only  be 
collections  of  stars  at  great  distances  apart. 

The  nearest  approximation  to  such  an  appearance 
as  that  described  is  the  faint,  diffused  light  of  the 
Milky  Way.  But  so  large  a  fraction  of  this  illumin- 
ation comes  from  the  stars  which  we  actually  see  in 
the  telescope  that  it  is  impossible  to  say  whether  any 
visible  illumination  results  from  masses  of  stars  too 
faint  to  be  individually  seen.  Whether  the  cloud-like 
impressions  which  Barnard  has  found  on  long-ex- 
posed photographs  of  the  Milky  Way  are  produced 
by  countless  distant  stars,  too  faint  to  impress 
themselves  individually  even  upon  the  most  sensitive 
photographic  plate,  is  a  question  which  cannot  yet 
be  answered.  But  even  if  we  should  answer  it  in 
the  affirmative,  the  extreme  faintness  of  the  light 


SS  THE  UNIVERSE  INFINITE!  231 

shows  that  the  stars  which  produce  it  are  not*  scat- 
tered through  infinite  space  ;  but  that,  although  they 
may  extend  much  beyond  the  limits  of  the  visible  stars, 
they  thin  out  very  rapidly.  The  evidence,  therefore, 
seems  to  be  against  the  hypothesis  that  the  stars  we 
see  form  part  of  an  infinitely  extended  universe. 

But  there  are  two  limitations  to  this  conclusion. 
It  rests  upon  the  hypothesis  that  light  is  never  lost 
in  its  passage  to  any  distance,  however  great.  This 
hypothesis  is  in  accordance  with  our  modern  theories 
of  physics,  yet  it  cannot  be  regarded  as  an  established 
fact  for  all  space,  even  if  true  for  the  distances  of  the 
visible  stars.  About  half  a  century  ago  Struve  pro- 
pounded the  contrary  hypothesis  that  the  light  of 
the  more  distant  stars  suffers  an  extinction  in  its 
passage  to  us.  But  this  had  no  other  basis  than  the 
hypothesis  that  the  stars  were  equally  thick  out  to 
the  farthest  limits  at  which  we  could  see  them.  It 
might  be  said  that  he  assumed  an  infinite  universe, 
and,  from  the  fact  that  he  did  not  see  the  evi- 
dence of  infinity,  concluded  that  light  was  lost. 
The  hypothesis  of  a  limited  universe  and  no  ex- 
tinction of  light,  while  not  absolutely  proved,  must 
be  regarded  as  the  one  to  be  accepted  until  further 
investigation  shall  prove  its  unsoundness. 

The  second  limitation  arises  from  the  possible 
structure  of  an  infinite  universe.  The  mathematical 
reader  will  easily  see  that  the  conclusion  that  an  in- 
finite universe  of  stars  would  fill  the  heavens  with  a 
blaze  of  light,  rests  upon  the  hypothesis  that  every 
region  of  space  of  some  great  but  finite  extent  is,  on 


23 2  STRUCTURE  OF  THE  HEAVENS 

the  average,  occupied  by  at  least  one  star.  In  other 
words,  the  hypothesis  is  that,  if  we  divide  the  total 
number  of  the  stars  by  the  number  of  cubic  miles  of 
space,  we  shall  have  a  finite  quotient.  But  an  infin- 
ite universe  can  be  imagined  which  does  not  fill  this 
condition.  Such  will  be  the  case  with  one  con- 
structed on  the  celebrated  hypothesis  of  Lambert,  pro- 
pounded in  the  latter  part  of  the  eighteenth  century. 
This  author  was  an  eminent  mathematician  who 
seems  to  have  been  nearly  unique  in  combining  the 
mathematical  and  the  speculative  sides  of  astronomy. 
He  assumed  a  universe  constructed  on  an  extension 
of  the  plan  of  the  solar  system.  The  smallest  sys- 
tem of  bodies  is  composed  of  a  planet  with  its  sat- 
ellites. We  see  a  number  of  such  systems,  designated 
as  the  Terrestrial,  the  Martian  (Mars  and  its  sat- 
ellites), the  Jovian  (Jupiter  and  its  satellites),  etc.,  all 
revolving  round  the  sun,  and  thus  forming  one 
greater  system,  the  solar  system.  Lambert  extended 
the  idea  by  supposing  that  a  number  of  solar  systems, 
each  formed  of  a  star  with  its  revolving  planets  and 
satellites,  were  grouped  into  a  yet  greater  system. 
A  number  of  such  groups  form  the  great  system 
which  we  call  the  galaxy,  and  which  comprises  all 
the  stars  we  can  see  with  the  telescope.  The  more 
distant  clusters  may  be  other  galaxies.  All  these 
systems  again  may  revolve  around  some  distant 
centre,  and  so  on  to  an  indefinite  extent.  Such  a 
universe,  how  far  so  ever  it  might  extend,  would  not 
fill  the  heavens  with  a  blaze  of  light,  and  the  more 
distant  galaxies  might  remain  for  ever  invisible  to  us. 


AS  THE  UNIVERSE  INF  I  NIT  F.I  233 

But  modern  developments  show  that  there  is  no 
scientific  basis  for  this  conception,  attractive  though 
it  be  by  its  grandeur. 

So  far  as  our  present  light  goes,  we  must  conclude 
that,  although  we  are  unable  to  set  absolute  bounds 
to  the  universe,  yet  the  great  mass  of  stars  is  in- 
cluded within  a  limited  space  the  extent  of  which  we 
have  as  yet  no  evidence.  Outside  of  this  space  there 
may  be  scattered  stars  or  invisible  systems.  But  if 
these  systems  exist,  they  are  distinct  from  our  own. 

The  second  question,  that  of  the  arrangement  of 
the  stars  in  space,  is  one  on  which  it  is  equally  diffi- 
cult to  propound  a  definite  general  conclusion.  So 
far,  we  have  only  a  large  mass  of  faint  indications, 
based  on  researches  which  cannot  be  satisfactorily 
completed  until  great  additions  are  made  to  our  fund 
of  knowledge. 

A  century  ago  Sir  William  Herschel  reached  the 
conclusion  that  our  universe  was  composed  of  a  com 
paratively  thin  but  widely  extended  stratum  of  stars. 
To  introduce  a  familiar  object,  its  figure  was  that  of 
a  large,  thin  grindstone,  our  solar  system  being  near 
the  centre.  Considering  only  the  general  aspect  of 
the  heavens,  this  conclusion  was  plausible.  Suppose 
a  mass  of  a  million  of  stars  scattered  through  a  space 
of  this  form.  It  is  evident  that  an  observer  in  the 
centre,  when  he  looked  through  the  side  of  the  stratum, 
would  see  few  stars.  The  latter  would  become  more 
and  more  numerous  as  he  directed  his  vision  toward 
the  circumference  of  the  stratum.  In  other  words, 
assuming  the  universe  to  have  this  form,  we  should 


234 


STRUCTURE  OF  THE  HEAVENS 


see  a  uniform,  cloud-like  arch  spanning  the  heavens — 
a  galaxy  in  fact. 

This  view  of  the  figure  of  the  universe  was  also 
adopted  by  Struve,  who  was,  the  writer  believes,  the 
first  astronomer  after  Herschel  to  make  investigations 
which  can  be  regarded  as  constituting  an  important 
addition  to  thought  on  the  subject.  To  a  certain  ex- 
tent we  may  regard  the  hypothesis  as  incontestable. 
The  great  mass  of  the  visible  stars  is  undoubtedly 
contained  within  such  a  figure  as  is  here  supposed. 

To  show  this  let  Fig.  i  represent  a  cross  section  of 
the  heavens  at  right  angles  to  the  Milky  Way,  the 


_„ p 

FIG.  1. 

solar  system  being  in  the  centre.  It  is  an  observed 
fact  that  the  stars  are  vastly  more  numerous  in 
the  galactic  regions  G  G  than  in  the  regions  P  P. 
Hence,  if  we  suppose  the  stars  equally  scattered,  they 
must  extend  much  farther  out  in  G  G  than  in  P  P.  If 
they  extend  as  far  in  the  one  direction  as  in  the  other, 
then  they  must  be  more  crowded  in  the  galactic  belt. 
It  will  still  remain  true  that  the  greater  number  of  the 
stars  are  included  in  the  flat  region  G  G  P  P,  those  out- 
side this  stratum  being  comparatively  few  in  number. 
But  we  cannot  assume  that  this  hypothesis  of  the 
form  of  the  universe  affords  the  basis  for  a  satisfactory 


FORM  OF  THE  UNIVERSE  235 

conception  of  its  arrangement.  Were  it  the  whole 
truth,  the  stars  would  be  uniformly  dense  along  the 
whole  course  of  the  Milky  Way.  Now,  it  is  a  familiar 
fact  that  this  is  not  the  case.  The  Milky  Way  is  not 
a  uniformly  illuminated  belt,  but  a  chain  of  irregular 
cloud-like  aggregations  of  stars.  Starting  from  this 
fact  as  a  basis,  our  best  course  is  to  examine  the  most 
plausible  hypotheses  we  can  make  as  to  the  distribu- 
tion of  the  stars  which  do  not  belong  to  the  galaxy, 
and  see  which  agrees  best  with  observation. 

Let   figure   2  represent  a  section   of  the  galactic 
ring  or  belt  in  its  own  plane,  with  the  sun  near  the 


\ 


si 

$       /"'  "N 

V.     i    s    • 


*i  + 


•A        SRi        it:        B 


»    ***  V#*  \ 

•»»*>  .  *S+  \ 


-W—^£r 


FIG.  2.  FiG.  3. 

centre,  S.  To  an  observer  at  a  vast  distance  in  the 
direction  of  either  pole  of  the  galaxy,1  the  latter  would 
appear  of  this  form.  Let  Fig.  3  represent  a  cross 

1  Regarding  the  galaxy  as  a  belt  spanning  the  heavens,  the  central  line  of 
which  is  a  great  circle,  the  poles  of  the  galaxy  are  the  two  opposite  points  in  the 
heavens  everywhere  90°  from  this  great  circle.  Their  direction  is  that  of  the 
two  ends  of  the  axle  of  the  grindstone,  as  seen  by  an  observer  in  the  centre, 
while  the  galaxy  would  be  the  circumference  of  the  stone. 


2  36  S  TR  UC  TURE  OF  THE  HE  A  VENS 

section  as  viewed  by  an  observer  in  the  plane  of  the  gal- 
axy at  a  great  distance  outside  of  it.  How  would  the 
stars  that  do  not  belong  to  the  galaxy  be  situated  ? 
We  may  make  three  hypotheses  : 

1.  That  they  are  situated  in  a  sphere  (A  B)  as  large 
as  the  galaxy  itself.      Then  the  whole  universe   of 
stars  would  be    spherical   in  outline,  and  the  galaxy 
would  be  a  dense  belt  of  stars  girdling  the  sphere. 

2.  The  remaining  stars  may  still  be  contained  in  a 
spherical  space  (K  L),  of  which  the  diameter  is  much 
less  than  that  of  the  galactic  girdle.      In  this  case  our 
sun  would  he  one  of  a  central  agglomeration  of  stars, 
lying  in  or  near  the  plane  of  the  galaxy. 

3.  The  non-galactic  stars  may  be  equally  scattered 
throughout  a  flat  region  (M  N  P  Q),  of  the  grindstone 
form.     This  would  correspond  to  the  hypothesis  of 
Herschel  and  Struve. 

There  is  no  likelihood  that  either  of  these  hypotheses 
is  true  in  all  the  geometric  simplicity  with  which 
I  have  expressed  it.  Stars  are  doubtless  scat- 
tered to  some  extent  through  the  whole  region  M  N 
P  Q,  and  it  is  not  likely  that  they  are  confined  within 
limits  defined  by  any  geometrical  figure.  The  most 
that  can  be  done  is  to  determine  to  which  of  the 
three  figures  the  mutual  arrangement  most  nearly 
corresponds. 

The  simplest  test  is  that  of  the  third  hypothesis  as 
compared  with  the  other  two.  If  the  third  hypo- 
thesis be  true,  then  we  should  see  the  fewest  stars 
in  the  direction  of  the  poles  of  the  galaxy  ;  and  the 
number  in  any  given  portion  of  the  celestial  sphere. 


FORM  OF  THE  UNIVERSE  237 

say  one  square  degree,  should  continually  increase, 
slowly  at  first,  more  rapidly  afterwards,  as  we  went 
from  the  poles  toward  the  circumference  of  the 
galaxy.  At  a  distance  of  60°  from  the  poles  and 
30°  from  the  central  line  or  circumference  we  should 
st;e  perhaps  twice  as  many  stars  per  square  degree 
ar  near  the  poles. 

Were  it  possible  to  determine  the  distance  of  a 
star  as  readily  as  we  do  its  direction,  the  problem  of 
the  distribution  of  the  stars  in  space  would  be  at 
once  solved.  This  not  being  the  case,  we  must  first 
study  the  apparent  arrangement  of  the  stars  with 
respect  to  the  galaxy,  with  a  view  to  afterward  draw- 
ing such  conclusions  as  we  can  in  regard  to  their 
distance. 


CHAPTER  XV 

APPARENT  DISTRIBUTION  OF  THE  STARS 
IN  THE  SKY 

Zwei  Dingen  erfiillen  das  Gemuth  mit  immer  neuer  und  zunehmender 
Bewunderung  und  Erfurcht,  je  ofter  und  anhaltender  sich  das  Nachdenkung 
damit  beschaftigt  .  der  bestirnte  Himmel  iiber  mir  und  das  moralische 
Gesetz  in  mir. — KANT. 

OUR  question  now  is,  How  are  the  stars,  as  we 
see  them,  distributed  over  the  sky  ?  We  know 
in  a  general  way  that  there  are  vastly  more  stars 
round  the  belt  of  the  Milky  Way  than  in  the  re- 
mainder of  the  heavens.  But  we  wish  to  know  in 
detail  what  the  law  of  increase  is  from  the  poles  of 
the  galaxy  to  the  belt  itself. 

In  considering  any  question  of  the  number  of  stars 
in  a  particular  region  of  the  heavens,  we  are  met  by 
a  fundamental  difficulty.  We  can  set  no  limit  to 
the  minuteness  of  stars,  and  the  number  will  depend 
upon  the  magnitude  of  those  which  we  include  in 
our  count.  As  already  remarked,  there  are,  at  least 
up  to  a  certain  limit,  three  or  four  times  as  many 
stars  of  each  magnitude  as  of  the  magnitude  next 
brighter.  Now,  the  smallest  stars  that  can  be  seen, 
or  that  may  be  included  in  any  count,  vary  greatly 
238 


DISTRIBUTION  OF  LUCID  STARS  239 

with  the  power  of  the  instrument  used  in  making  the 
count.  If  we  had  any  one  catalogue,  extending  over 
the  whole  celestial  sphere,  and  made  on  an  absolutely 
uniform  plan,  so  that  we  knew  it  included  all  the 
stars  down  to  some  given  magnitude,  and  no  others, 
it  would  answer  our  immediate  purpose.  If,  however, 
one  catalogue  including  the  stars  in  a  certain  part  of 
the  sky  should  extend  only  to  the  ninth  magnitude, 
while  another,  covering  another  part,  should  extend 
to  the  tenth,  we  should  be  led  quite  astray  in  assum- 
ing that  the  number  of  stars  in  the  two  catalogues 
expressed  the  star  density  in  the  regions  which  they 
covered.  The  one  would  show  three  or  four  times 
as  many  stars  as  the  other,  even  though  the  actual 
density  in  the  two  cases  were  the  same. 

If  we  could  be  certain,  in  any  one  case,  just  what 
the  limit  of  magnitude  was  for  any  catalogue,  or  if 
the  magnitudes  in  different  catalogues  always  cor- 
responded to  absolutely  the  same  brightness  of  the 
star,  this  difficulty  would  be  obviated.  But  this  is 
the  case  only  with  that  limited  number  of  stars  whose 
brightness  has  been  photometrically  measured.  In 
all  other  cases  our  count  must  be  more  or  less  un- 
certain. One  illustration  of  this  will  suffice  : 

I  have  already  remarked  that  in  making  the  pho- 
tographic census  of  the  southern  heavens,  Gill  and 
Kapteyn  did  not  assume  that  stars  of  which,  the 
images  were  equally  intense  on  different  plates  were 
actually  of  the  same  magnitude.  Each  plate  was 
assumed  to  have  a  scale  of  its  own,  which  was  fixed  by 
comparing  the  intensity  of  the  photographic  impres- 


24o       APPARENT  DISTRIBUTION  OF  STARS 

sions  of  those  stars  whose  magnitudes  had  been 
previously  determined  with  these  determinations,  and 
thus  forming  as  it  were  a  separate  scale  for  each 
plate.  But,  in  forming  the  catalogue  from  the  inter- 
national photographic  chart  of  the  heavens,  it  is 
assumed  that  the  photographs  taken  with  telescopes 
of  the  same  aperture,  in  which  the  plates  are  exposed 
for  five  minutes,  will  all  correspond,  and  that  the 
smallest  stars  found  on  the  plates  will  be  of  the 
eleventh  magnitude. 

In  the  case  of  the  lucid  stars  this  difficulty  does 
not  arise,  because  the  photometric  estimates  are  on  a 
Distribution  sufficiently  exact  and  uniform  scale  to 
of  the  Lucid  enable  us  to  make  a  count,  which  shall  be 
nearly  correct,  of  all  the  stars  down  to,  say, 
magnitude  6.0  or  some  limit  not  differing  greatly 
from  this.  Several  studies  of  the  distribution  of  these 
stars  have  been  made ;  one  by  Gould  in  the  Urano- 
metria  Argentina,  one  by  Schiaparelli,  and  another 
by  Pickering.  The  counts  of  Gould  and  Schiaparelli, 
the  former  having  special  reference  to  the  Milky 
Way,  are  best  adapted  to  our  purpose.  The  most 
striking  result  of  these  studies  is  that  the  condensa- 
tion in  the  Milky  Way  seems  to  commence  with  the 
brightest  stars.  A  little  consideration  will  show  that 

& 

we  cannot,  with  any  probability,  look  for  such  a  con- 
densation in  the  case  of  stars  near  to  us.  Whatever 
form  we  assign  to  the  stellar  universe,  we  shall  expect 
the  stars  immediately  around  us  to  be  equally  dis- 
tributed in  every  direction.  Not  until  we  approach 
the  boundary  of  the  universe  in  one  direction,  or  some 


is.STRIBUTlON  OF  LUCID  STARS  241 

great  masses  like  those  of  the  galaxy  in  another 
direction,  should  we  expect  marked  condensation 
round  the  galactic  belt.  Of  course  we  might  imagine 
even  the  nearest  stars  to  be  most  numerous  in  the 
direction  round  the  galactic  circle.  But  this  would 
imply  an  extremely  unlikely  arrangement,  our  system 
being  as  it  were  at  the  point  of  a  conical  region 
richer  in  stars  than  the  region  around  it.  It  is  clear 
that  if  such  were  the  case  for  one  point,  it  could  not 
be  true  if  our  sun  were  placed  anywhere  except  at 
this  particular  point.  Such  an  arrangement  of  the 
stars  round  us  is  outside  of  all  reasonable  probability. 
Independent  evidence  of  the  equal  distribution  of  the 
nearer  stars  will  hereafter  be  found  in  the  proper 
motions.  If,  then,  the  nearer  stars  are  equally  dis- 
tributed round  us,  and  only  distant  ones  can  show 
a  condensation  toward  the  Milky  Way,  it  follows  that 
among  the  distant  stars  are  some  of  the  brightest  in 
the  heavens,  a  fact  which  we  have  already  shown  to 
follow  from  other  considerations. 

As  we  have  to  study  the  distribution  of  the  stars 
with  respect  to  the  galaxy,  the  precise  position  of  the 
latter  enters  into  our  problem.  There  is  no  difficulty 
in  mapping  out  its  general  course  by  unaided  eye 
observations  of  the  heavens  or  a  study  of  maps  of  the 
stars.  Looking  at  the  heavens,  we  shall  readily  see 
that  it  crosses  the  equator  at  two  opposite  points  ;  the 
one  east  of  the  constellation  Orion,  between  6h.  and 
7h.  of  right  ascension  ;  the  other  at  the  opposite  point, 
in  Aquila,  between  i8h.  and  igh.  It  makes  a  con- 
siderable angle  with  the  equator,  somewhat  more  than 

16 


242       APPARENT  DISTRIBUTION  OF  STARS 

60°.  Consequently  it  passes  within  30°  of  either 
celestial  pole.  The  point  nearest  of  approach  to  the 
north  pole  is  in  the  constellation  Cassiopeia. 

Its  position  can  readily  be  determined  by  noting- 
the  general  course  of  its  brighter  portions  on  a  map 
of  the  stars,  and  then  determining,  by  inspection  or 
otherwise,  the  circle  which  will  run  most  nearly 
through  those  portions.  It  is  thus  found  that  the 
position  is  nearly  always  near  a  great  circle  of 
the  sphere.  From  the  very  nature  of  the  case  the 
position  of  this  circle  will  be  a  little  indefinite,  and 
probably  the  estimates  made  of  it  have  been  based 
more  on  inspection  than  on  computation.  The  fol- 
lowing positions  have  been  assigned  to  the  pole  of 
the  galaxy : 

Gould R.  A.  =  izh.  4im.  Dec.  =  -f-  27°  21' 

Herschel,  W  ....               "  i2h.   29m.  '  +31°  30' 

Seeliger "        "  i2h.  49111.  '   +  27°  3°' 

Argelander "        "  i2h.  4om.  '   +28°     5' 

The  author,  with  the  assistance  of  Mr.  Wm.  T.  Car- 
rigan,  has  made  an  independent  determination  by  find- 
ing the  great  circle  which  will  pass  nearest  to  some 
40  of  the  brightest  regions  of  the  galaxy.  The  result 
is  different  according  as  we  include  or  omit  the  diver- 
gent branch  toward  the  west  between  Cygnus  and 
Aquila.  Including  the  branch,  the  position  of  the 
galactic  pole  is, 

R.  A.  =  i2h.  44m.     Dec.  =  26°  48' 
Excluding  the  branch  it  is, 

R.  A.  =  i2h.  51111.     Dec.  =   27°  12' 


DISTRIBUTION  OF  LUCID  STARS  243 

Very  remarkable  is  the  fact,  first  pointed  out  by  Sir 
J.  Herschel,  and  more  fully  developed  by  Gould,  that 
a  belt  of  bright  stars  encircles  the  heavens  but  does 
not  exactly  coincide  with  the  Milky  Way.  It  inter- 
sects the  galaxy  at  the  points  nearest  the  celestial 
poles,  one  node  being  near  the  Southern  Cross  and 
the  other  in  Cassiopeia.  This  belt  includes  the 
brightest  stars  in  a  number  of  constellations,  from 
Canis  Major  through  the  southern  region  of  the 
heavens  and  back  to  Scorpius.  In  the  northern 
heavens  the  brightest  stars  in  Orion,  Taurus,  Cas- 
siopeia, Cygnus,  and  Lyra  belong  to  it.  It  would  not 
be  safe,  however,  to  assume  that  the  existence  of 
this  belt  results  from  anything  but  the  chance  dis- 
tribution of  the  few  bright  stars  which  form  it.  In 
order  to  reach  a  definite  conclusion  bearing  on  the 
structure  of  the  heavens,  it  is  advisable  to  consider  the 
distribution  of  the  lucid  stars  as  a  whole. 

Dr.  Gould  found  that  the  stars  brighter  than  the 
fourth  magnitude  are  arranged  more  symmetrically 
relatively  to  the  belt  of  bright  stars  we  have  just  de- 
scribed than  to  the  galactic  circle.  This  and  other  facts 
suggested  to  him  the  existence  of  a  small  cluster  within 
which  our  sun  is  eccentrically  situated,  and  which  is 
itself  not  far  from  the  middle  plane  of  the  galaxy. 
This  cluster  appears  to  be  of  a  flattened  shape  and  to 
consist  of  somewhat  more  than  400  stars  of  magni- 
tudes ranging  from  the  first  to  the  seventh.  Since 
Gould  wrote,  the  extreme  inequality  in  the  intrinsic 
brightness  of  the  stars  has  been  brought  to  light  and 
seems  to  weaken  his  explanation  of  the  fact. 


244       APPARENT  DISTRIBUTION  OF  STARS 

A  very  thorough  study  of  the  subject,  but  without 
considering  the  galaxy,  has  also  been  made  by 
Schiaparelli.  The  work  is  based  on  the  photometric 
measures  of  Pickering  and  the  Uranometria  Argen- 


STAR-DENSITY  OF  THE  NORTHERN  HEMISPHERE 

tina  of  Gould.  One  of  its  valuable  features  is  a  series 
of  planispheres,  showing  in  a  visible  form  the  star 
density  in  every  region  of  the  heavens  for  stars  of 
various  magnitudes.  We  reproduce  on  a  reduced  scale 
two  of  these  planispheres.  They  were  constructed  by 
Schiaparelli  in  the  following  way  :  The  entire  sky 


DISTRIBUTION  OF  LUCID  STARS 


245 


was  divided  into  36  zones  by  parallels  of  declination 
5°  apart.  Each  zone  was  divided  into  spherical 
trapezia  by  hour-circles  taken  at  intervals  of  5°  from 
the  equator  up  to  50°  of  north  or  south  declination ; 


STAR-DENSITY  OF  THE  SOUTHERN  HEMISPHERE 

of  10°  from  50  to  60  ;  of  15°  from  60  to  80  ;  of  45°  from 
80  to  85,  while  the  circle  within  5°  of  the  pole  was 
divided  into  four  regions.  In  this  way  1800  areas, 
not  excessively  different  from  each  other,  were  formed. 
The  star-density,  as  it  actually  is,  might  be  indicated 


246       APPARENT  DISTRIBUTION  OF  STARS 

by  the  number  of  stars  of  these  regions.  As  a  matter 
of  fact,  however,  the  density  obtained  in  this  way 
would  vary  too  rapidly  from  one  area  to  the  adjoining 
one,  owing  to  the  accidental  irregularities  of  distribu- 
tion of  the  stars.  An  adjustment  was,  therefore,  made 
by  finding  in  the  case  of  each  area  the  number  of 
stars  contained  in  i  /  200  of  the  entire  sphere,  includ- 
ing the  region  itself  and  those  immediately  around  it. 
The  number  thus  obtained  was  considered  as  giving 
the  density  for  the  central  region.  The  total  number 
of  stars  being  4303,  the  mean  number  in  i  /  200  of  the 
whole  sphere  is  21.5,  and  the  mean  in  each  area  is  10.4. 

The  numbers  on  the  planisphere  given  in  each  area 
express  the  star  density  of  the  region,  or  the  number 
of  stars  per  100  square  degrees,  expressed  generally  to 
the  nearest  unit,  the  half-unit  being  sometimes  added. 

A  study  of  the  reproduction  which  we  give  will 
show  how  fairly  well  the  Milky  Way  may  be  traced 
out  round  the  sky  by  the  tendency  of  those  stars 
visible  to  the  naked  eye  to  agglomerate  near  its  course. 
In  other  words,  were  the  cloud-forms  which  make  up 
the  Milky  Way  invisible  to  us,  we  should  still  be  able 
to  mark  out  its  course  by  the  crowding  of  the  lucid 
stars  toward  it.  As  a  matter  of  interest,  I  have  traced 
out  the  central  line  of  the  darker  shaded  portions  of  the 
planispheres  as  if  they  were  the  galaxy  itself.  The 
nearest  great  circle  to  the  course  of  this  line  was  then 
found  to  have  its  pole  in  the  following  position : 

R.  A.;  I2h.  i8m. 
Dec.  +  27°. 

This  estimate  was  made  without  having  at  the  time 


DISTRIBUTION  OF  FAINTER  STARS          247 

any  recollection  of  the  position  of  the  galaxy  given  by 
other  authorities.  Compared  with  the  positions  given 
in  the  last  chapter  by  Gould  and  Seeliger,  it  will  be 
seen  that  the  deviation  is  only  5°  in  right  ascension, 
while  the  declinations  are  almost  exactly  similar. 
We  infer  that  the  circle  of  condensation  found  in 
this  way  makes  an  angle  with  the  galaxy  of  less 
than  5°. 

The  most  thorough  study  of  the  distribution  of  the 
great  mass  of  stars  relative  to  the  galactic  plane  has 
been  made  by  Seeliger  in  a  series  of  papers  Distribution 
presented  to  the  Munich  Academy  from  oftheFaint- 
1 884  to  1 898.  The  data  on  which  they  are  er  stars> 
based  are  the  following  : 

1.  The  Botmer  DurchmusterungQi  Argelander  and 
Schonfeld,  described  in  our  third  chapter.     The  two 
works  under  this  title  are  supposed  to  include  all  the 
stars  to  the  ninth  magnitude,  from  the  north  pole  to 
24°  of  south  declination.      But  there  are  some  incon- 
sistencies in  the  limit  of  magnitude  which  we  shall 
hereafter  mention. 

2.  The  "  star  gauges  "  of  the  two  Herschels.    These 
consisted  simply  in  counts  of  the  number  of  stars  visi- 
ble in  the  field  of  view  of  the  telescope  when  the  lat- 
ter was  directed   toward  various  regions  of  the  sky. 
Sir  William  Herschel's  gauges  were  partly  published 
in  the  Philosophical  Transactions.     A  number  of  un- 
published  ones   were    found    among    his    papers    by 
Holden  and  printed  in  the  publications  of  the  Wash- 
burn  Observatory,  vol.   ii.     The  younger   Herschel, 
during  his  expedition  to  the  Cape  of  Good   Hope, 


248        APPARENT  DISTRIBUTION  OF  STARS 

continued  the  work  in  those  southern  regions  of  the 
sky  which  could  not  be  seen  in  England. 

3.  A  count  of  the  stars  by  Celoria,  of  Milan,  in  a 
zone  from  the  equator  to  6°  N.  Dec.,  extending  round 
the  heavens. 

From  what  has  been  said,  the  first  question  to  oc- 
cupy our  attention  is  that  of  the  distribution  of  the 
stars  with  reference  to  the  galactic  plane,  or,  rather, 
the  great  circle  forming  the  central  line  of  the  Milky 
Way. 

The  whole  sky  is  divided  by  Seeliger  into  nine 
zones  or  regions,  each  20°  in  breadth,  by  small  circles 
parallel  to  the  galactic  circle.  Region  I.  is  a  circle  of 
20°  radius,  whose  centre  is  the  north  galactic  pole.. 
Round  this  central  circle  is  a  zone  20°  in  breadth, 
called  zone  II.  Continuing  the  division,  it  will  be 
seen  that  zone  V.  is  the  central  one  of  the  Milky  Way, 
extending  10°  on  each  side  of  the  galactic  circle.  VI. 
is  the  zone  next  south  of  the  galaxy,  and  so  on  to  IX., 
which  is  the  circle  40°  in  diameter  round  the  south 
galactic  pole. 

The  condensed  result  of  the  work  is  shown  in  the 
following  table. 

Column  "  Area  "  shows  the  number  of  square  de- 
grees in  each  region,  so  far  as  included  in  the  survey. 
It  will  be  remarked  that  the  catalogues  in  question  do 
not  include  the  whole  sky,  as  they  stop  at  24°  S.Dec. 

Column  "Stars"  shows  the  number  of  stars  to 
magnitude  9.0  found  in  each  area. 

Column  "  Density  "  is  the  quotient  of  the  number  of 
stars  by  the  area,  and  is,  therefore,  the  mean  number 


DISTRIBUTION  OF  FAINTER  STARS         249 

of  stars  per  square  degree  in  each  region.  In  the  last 
column  these  numbers  are  corrected,  for  certain  anom- 
alies in  the  magnitudes  given  by  the  catalogues,  so  as 
to  reduce  them  to  a  common  standard. 

Area.  Corrected 

Region.                      Degrees.  Stars.         Densicy.  Density. 

I i,398.7  4,277  3-°6  2-78 

II 3^46.9  10,185  3-24  3-°3 

III... 5,126.6  19,488  3.80  3.54 

IV...'. 4,589-8  24,492  5.34  5.32 

V 4,5*9-5  33,267  7-36  8.17 

VI 3,97i-5  23,580  5.94  6.07 

VII...  = 2,954.4  11,79°  3-99  3-7i 

VIII i,79°-6  6»375  3-56  3-2i 

.  IX 468.2  1,644  3-51  3-I4 

A  study  of  the  last  two  columns  is  decisive  of  one 
of  the  fundamental  questions  already  raised.  The 
star-density  in  the  several  regions  increases  continu- 
ously from  each  pole  (regions  I.  and  IX.)  to  the 
galaxy  itself.  If  the  latter  were  a  simple  ring  of  stars 
surrounding  a  spherical  system  of  stars,  the  star- 
density  would  be  about  the  same  in  regions  I.,  II., 
and  III.,  and  also  in  VII.,  VIII.,  and  IX.,  but  would 
suddenly  increase  in  IV.  and  VI.  as  the  boundary  of 
the  ring  was  approached.  Instead  of  such  being  the 
case,  the  numbers  2.78,  3.03,  and  3.54  in  the  north, 
and  3.14,  3.21,  and  3.71  in  the  south,  show  a  progres- 
sive increase  from  the  galactic  pole  toward  the  galaxy 
itself.- 

The  conclusion  to  be  drawn  is  a  fundamental  one. 
The  universe,  or,  at  least,  the  denser  portions  of  it, 
is  really  flattened  between  the  galactic  poles,  as  sup- 


250      APPARENT  DISTRIBUTION  OF  STARS 

posed  by  Herschel  and  Struve.  In  the  language  of 
Seeliger :  "The  Milky  Way  is  no  merely  local  phe- 
nomenon, but  is  closely  connected  with  the  entire 
constitution  of  our  stellar  system." 

This  conclusion  is  strengthened  by  a  study  of  the 
data  given  by  Celoria.  It  will  be  remarked  that  the 
zone  counted  by  this  astronomer  cuts  the  Milky  Way 
diagonally  at  an  angle  of  about  62°,  and,  therefore, 
does  not  take  in  either  of  its  poles.  Consequently, 
regions  I.  and  IX.  are  both  left  out.  For  the  re- 
maining seven  regions  the  results  are  shown  as  fol- 
lows :  We  show  first  the  area,  in  square  degrees,  of 
each  of  the  regions,  II.  to  VIII.,  included  in  Celoria's 
zone.  Then  follows  in  the  next  column  the  number 
of  stars  counted  by  Celoria,  and,  in  the  third,  the 
number  enumerated  in  the  Durclimusterung,  in  these 
portions  of  each  region.  The  quotients  show  the 
star-density,  or  the  mean  number  of  stars  per  square 
degree,  recorded  by  each  authority  : 

Area.  Number  of  Stars.  Star-Density. 

Region.  Degrees.          Cel.  D.  M.  Cel.        D.  M. 

II 404-4  27,352  1,230  67.6  3.04 


III  

2846 

22   Cqi 

032 

7Q.  7 

3.28 

IV  

.  .  2^4  6 

2O  460 

488 

I  rc.7 

S  8* 

V  

284  6 

41  820 

8n 

146  q 

644 

VI  

.  .  284  6 

•j  i  706 

472 

1  1  1  4 

<  22 

VII   .    . 

.  .  320  ^ 

25  618 

142 

77  7 

4  O? 

VIII.. 

..314.* 

22.264 

.184 

708 

1.79 

It  will  be  seen  that  the  law  of  increasing  star-density 
from  near  the  galactic  pole  to  the  galaxy  itself  is 
of  the  same  general  character  in  the  two  cases.  The 


DISTRIBUTION  OF  FAINTER  STARS          251 

number  of  stars  counted  by  Celoria  is  generally  be- 
tween 1 8  and  25  times  the  number  in  the  Durch- 
musterung. 

An  important  point  to  be  attended  to  hereafter  is 
that  the  star-density  of  the  Milky  Way  itself,  as 
found  by  Celoria  and  the  authors  of  the  Ditrch- 
musterung,  is  between  two  or  three  times  that  near 
the  galactic  poles.  Very  different  is  the  result  de- 
rived from  the  Herschelian  gauges,  which  is  this  : 

Region....!.  II.  III.  IV.  V.  VI.  VII.  VIII.  IX. 
Density. ..  107  154  281  560  2019  672  261  154  in 

From  the  gauges  of  the  Herschels  it  follows  that 
the  galactic  star-density  is  nearly  20  times  that  near 
the  galactic  poles.  At  these  poles  the  Herschels 
counted  only  about  50  per  cent,  more  stars  than  Celoria. 
In  the  galaxy  itself  they  counted  14  for  every  one  by 
Celoria.  There  is  little  doubt  as  to  the  principal 
cause  of,  this  discrepancy.  The  observations  by  the 
first  two  authorities  were  made  with  smaller  telescopes 
than  that  of  Herschel,  and  they  failed  to- count  all  the 
visible  stars  of  the  Milky  Way.  The  recent  compari- 
sons of  the  JDurchimtsterungvj\t\\.  the  heavens,  mostly 
made  since  Seeliger  worked  out  the  results  we  have 
given,  show  that  the  limit  of  magnitude  to  which  this 
list  extends  is  far  from  uniform,  and  varies  with  the 
star-density.  In  regions  poor  in  stars,  all  of  the 
latter  to  the  tenth  magnitude  are  listed  ;  in  the  richer 
regions  of  the  galaxy  the  list  stops,  we  may  suppose, 
with  the  ninth  magnitude,  or  even  brighter.  Yet,  in 
all  cases,  the  faintest  stars  listed  are  classed  as  of 


252       APPARENT  DISTRIBUTION  OF  STARS 

magnitude  9.5.  Thus  a  ninth-magnitude  star  in  the 
galaxy,  according  to  the  Durchmusterung,  is  markedly 
brighter  than  one  of  this  magnitude  elsewhere. 

Having  found  that  the  stars  of  every  magnitude 
show  a  tendency  to  crowd  toward  the  region  of  the 
Distribu-  Milky  Way,  the  question  arises  whether  this 
tionofthe  is  true  of  those  stars  which  have  a  sensible 
stars  hav-  prOper  motiOn.  Kaptevn  has  examined  this 

ing  Sensi-     '  * 

bie  Proper  question  in  the  case  of  the  Bradley  stars. 
Motio.i.  j_jjs  conclusion  is  that  those  having  a  con- 
siderable proper  motion,  say  more  than  5"  per  cent- 
ury, are  nearly  equally  distributed  over  the  sky,  but 
that  when  we  include  those  having  a  small  proper 
motion,  we  see  a  continually  increasing  tendency  to 
crowd  toward  the  galactic  plane. 

It  seems  to  the  writer  that  the  uncertainty  as  to 
the  smaller  proper  motions  of  the  Bradley  stars  ren- 
ders this  result  quite  unreliable.  To  reach  a  more 
definite  conclusion,  we  must  base  our  work  on  lists 
of  proper  motions  which  are  as  nearly  complete 
within  their  limits  as  it  is  possible  to  make  them. 
Such  lists  have  been  made  by  Auwers  and  Boss,  their 
work  being  based  on  their  observations  of  zones  of 
stars  for  the  catalogue  of  the  Astronomische  Gesell- 
schaft.  The  zone  observed  by  Auwers  was  that  be- 
tween 15°  and  20°  of  N.  Dec.;  while  Boss's  was 
between  i°  and  5°.  To  speak  more  exactly,  the 
limits  were  from  14°  50'  to  20°  10'  and  o°  50'  to  5° 
10',  each  zone  of  observation  overlapping  10'  on  the 
adjoining  one.  Thus  the  actual  breadths  were  5°  20' 
and  4°  20'.  Within  these  respective  limits,  Auwers, 


PROPER-MOTION  STARS  253 

by  a  comparison  with  previous  observations,  found 
1300  stars  having  an  appreciable  proper  motion,  and 
Boss  295.  But  Boss's  list  is  confined  to  stars  having 
a  motion  of  at  least  10";  of  such  the  list  of  Auwers 
contains  431.  The  number  of  square  degrees  in  the 
two  zones  is  1556  and  1830,  respectively.  The  cor- 
responding number  of  stars  with  proper  motions  ex- 
tending 10"  is  for  each  100  square  degrees : 

In  Boss's  zone,  18.9. 
In  Auwers's  zone,  23.9. 

The  question  whether  the  greater  richness  of 
nearly  25  per  cent,  in  Auwers's  zone  is  real  is  one 
to  which  it  is  not  easy  to  give  a  conclusive  answer. 
The  probability,  however,  seems  to  be  that  it  is 
mainly  due  to  the  greater  richness  of  the  material 
on  which  Auwers's  proper  motions  are  based.  Hap- 
pily, the  question  is  not  essential  in  the  present 
discussion. 

We  now  examine  the  question  of  the  respective 
richness  of  proper-motion  stars  in  this  way : 

Each  of  these  zones  cuts  the  galaxy  at  a  consider- 
able angle  in  two  opposite  regions.  Each  zone,  as  a 
matter  of  course,  has  a  far  greater  richness  of  stars 
per  unit  of  surface  in  the  two  galactic  regions  than 
in  the  intermediate  regions.  We,  therefore,  divide 
each  zone  in  four  strips,  two  including  the  galactic 
regions  and  two  the  intermediate  regions.  The 
boundaries  are  somewhat  indefinite ;  we  have  fixed 
them  by  the  richness  of  the  total  number  of  stars. 
For  the  galactic  strips  we  take  in  Boss's  zone  the 


254      APPARENT  DISTRIBUTION  OF  STARS 

strip  between  5h.  and  8h.  of  R.  A.  and  that  between 
I7h.  and  2oh.  Each  of  these  strips  being  3h.  in 
length,  the  two  together  comprise  one  quarter  the 
total  surface  of  the  zone.  If  the  proper-motion  stars 
crowd  towards  the  galaxy  like  others  do,  then  the 
numbers  in  the  galactic  region  should  be  proportional 
to  the  total  number  observed  in  the  region.  But 
if  they  are  equally  distributed,  then  there  should  be 
only  one  quarter  as  many  in  the  galactic  region  as  in 
the  other  regions. 

In  the  case  of  Boss's  zone,  the  total  number  of 
stars  observed,  and  of  those  having  a  proper  motion, 
found  in  the  four  regions  described,  are  as  follows : 

Star- 
Total  Number     Proper      Density 
Observed.      Motions,  per  hour. 

Galactic  strip,  5h.  to  8h i,6r4  24  8 

Galactic  strip,  i  yh.  to  2oh I,34°  36  12 

Intermediate  strip,  8h.  to  tyh 2,458  124  12 

Intermediate  strip,  2oh.  to  5 h 2,831  in  12 

The  last  column  contains  the  average  number  of 
proper-motion  stars  per  hour  in  each  of  the  four  strips. 
There  is  evidently  no  excess  of  richness  in  the  galactic 
strips,  but  rather  a  deficiency  in  the  strip  near  6h., 
which  we  may  regard  as  accidental. 

In  the  case  of  Auwers's  zone,  the  galactic  strips 
are  those  between  5h.  and  8h.,  and  again  between  i8h. 
and  2  ih.  Here,  as  in  the  other  case,  the  galactic  strips 
include  one  quarter  of  the  whole  area.  But,  owing 
to  the  greater  richness  of  the  sky,  they  include  nearly 
forty  per  cent,  of  the  whole  number  of  stars.  Then, 
if  the-proper  motion  stars  are  equally  distributed,  one- 


STARS  WITH  PROPER  MOTION  255 

quarter  should  be  found  in  the  galactic  regions,  and 
if  they  are  proportional  to  the  number  of  stars  ob- 
served, forty  per  cent,  should  be  within  these  regions. 
Grouping  the  regions  outside  the  galaxy  together,  as 
we  need  not  distinguish  between  them,  the  result  is 

as  follows : 

Star 

Stars  Proper    Density 

Observed.  Motions,  per  hour. 

Galactic  strip,  5h.  to  8h x,797  J55             52 

Galactic  strip,  i8h.  to  21  h 1,984  202             67 

Outside  the  galaxy 6,008  901             50 

We  see  that  in  the  galactic  strip  from  5h.  to  8h. 
there  is  contained  almost  exactly  one-eighth  the 
whole  number  of  proper-motion  stars.  That  is,  in 
this  region  the  stars  are  no  thicker  than  elsewhere. 
In  the  region  from  i8h.  to  2ih.  there  is  an  excess 
of  45  stars  having  proper  motions,  or  15  per  hour. 
Whether  this  excess  is  real  may  well  be  doubted.  It  is 
scarcely,  if  at  all,  greater  than  might  be  the  result  of 
accidental  inequalities  of  distribution.  Were  the 
proper-motion  stars  proportional  to  the  whole  num- 
ber, there  ought  to  be  240  within  the  strip.  The  actual 
number  is  38  less  than  this. 

It  is  to  be  remembered  that  Auwers's  proper  mo- 
tions are  not  limited  to  a  definite  magnitude,  as  were 
Boss's,  but  that  he  looked  for  all  stars  having  a  sensi- 
ble proper  motion.  The  question,  what  proper  mp- 
tion  would  be  sensible,  is  a  somewhat  indefinite  one, 
depending  very  largely  on  the  data.  It  may,  there- 
fore, well  be  that  the  small  excess  of  45  found  within 
this  strip  is  due  to  the  fact  that  more  stars  were 


256       APPARENT  DISTRIBUTION  OF  STARS 

observed  and  investigated,  and,  therefore,  more  proper 
motions  found.  Besides  this,  some  uncertainty  may 
exist  as  to  the  reality  of  the  minuter  proper  motions. 

The  conclusion  is  interesting  and  important.  If  we 
should  blot  out  from  the  sky  all  the  stars  having  no 
proper  motion  large  enough  to  be  detected,  we  should 
find  remaining  stars  of  all  magnitudes ;  but  they 
would  be  scattered  almost  uniformly  over  the  sky,  and 
show  little  or  no  tendency  to  crowd  toward  the  galaxy, 
unless,  perhaps,  in  the  region  near  igh.  of  R.  A. 

From  this  again  it  follows  that  the  stars  belonging 
to  the  galaxy  lie  farther  away  than  those  whose 
proper  motions  can  be  detected. 

Pickering  found  that  the  stars  of  the  fifth  spectral 
type,  or  of  Vogel's  class  II  b,  are  mostly  distributed 
Distribution  al°ng  tne  central  line  of  the  Milky  Way.  An 
of  Fifth-type  exception  occurs  in  the  case  of  a  group  situ- 
stars-  ate  in  the  "  Magellanic  clouds,"  a  cloud-like 

mass  of  small  stars  too  far  south  to  be  visible  in  our 
latitudes,  and  detached  from  the  main  course  of  the 
Milky  Way  itself.  The  total  number  of  the  stars  in 
question  is  91,  of  which  70  are  in  the  Milky  Way  and 
21  in  the  Magellanic  clouds. 

An  interesting  question  now  is  whether  the  70 
stars  along  the  Milky  Way  are  arranged  independently 
of  the  latter,  or  belong  to  its  agglomerations.  In  the 
latter  case  we  should  expect  to  find  most  of  the  stars 
in  the  densest  portions  of  the  galaxy  ;  in  the  former 
case  they  would  be  arranged  independently  of  the 
galactic  masses. 

The  actual  distribution  is  not  decidedly  in  favour  of 


FIFTH-TYPE  STARS  257 

either  view.  Groups  of  the  stars  are  found  here  and 
there  in  the  densest  spots  of  the  galaxy  ;  but  there 
are  also  a  number  in  the  very  darkest  regions  of  the 
central  line.  The  mean  distance  of  the  70  stars 
from  the  central  galactic  circle  is  2°.  6  ;  the  mean  dis- 
tance of  42  of  the  brightest  regions  of  the  galaxy 
from  the  same  circle  is  2°.  3.  The  central  circle  which 
passes  most  nearly  through  the  70  stars  has  its  pole 
in  the  position 

R.  A.  =  12  h.  44m.,  Dec.  =  -f-  26°.  6 
The  coincidence  of  this  with  the  galactic  circle  is  very 
close,  the  deviation  being  only  a  quarter  of  a  degree. 
Most  curious  is  the  unequal  distribution  of  these 
stars  around  the  galactic  circle.  Starting  from  the 
point  where  this  circle  crosses  the  equator  near  i8h. 
4om.  of  R.  A.,  and  going  toward  the  north  there  are 

In  the  first  quadrant  15  stars 

'    second    '  3     ' 

"     "    third        "         21     " 
"     "    fourth      "         31     " 

Thus  there  are  18  stars  in  the  first  semicircle  against 
52  in  the  second.  They  are  sometimes  bunched  to- 
gether ;  thus  in  R.  A.  zoh.  and  Dec.  —  60°  there  are 
13  of  the  stars  in  a  region  5°  square. 


CHAPTER  XVI 
THE  CLUSTERING  OF  THE  STARS 

The  stars  in  deep  amaze 

Stand  fixed  in  steadfast  gaze. 

Bending  one  way  their  precious  influence 

And  will  not  take  their  flight 

For  all  the  morning  light 

Or  Lucifer  that  often  warned  them  thence. 

A  STUDY  of  Schiaparelli's  planispheres,  found  in 
the  last  chapter,  shows  that  some  regions  of  the 
heavens  are  especially  rich  in  lucid  stars  and  others 
especially  poor. 

Neither  telescope  nor  planisphere  is  necessary  to 
show  that  many  of  those  stars  are  collected  in  clusters. 
That  the  Pleiades  form  a  group  of  stars  by  itself  is 
clear  from  the  consideration  that  six  stars  so  bright 
would  not  fall  so  close  together  by  accident.  This 
conclusion  is  confirmed  by  their  common  proper  mo- 
tion, different  from  that  of  the  stars  around  them. 
The  singular  collection  of  bright  stars  which  form 
Orion,  the  most  brilliant  constellation  in  the  heavens, 
and  the  little  group  called  Coma  Berenices — the  Hair 
of  Berenice — also  suggest  the  problem  of  the  possible 
connection  of  the  stars  which  form  them. 

The  question  we  now  propose  to  consider  is  whether 
these  clusters  include  within  their  limits  an  important 
258 


SMALL  STARS  IN  THE  PLEIADES  259 

number  of  the  small  stars  seen  in  the  same  direction. 
If  they  and  all  the  small  stars  which  they  contain 
within  their  actual  limits  were  removed  from  the  sky, 
would  important  gaps  be  left  ?  The  significance  of 
this  question  will  be  readily  seen.  If  important  gaps 
would  be  left,  it  would  follow  that  a  large  proportion 
of  the  stars  which  we  see  in  the  direction  of  the 
clusters  really  belong  to  the  latter,  and  that,  therefore, 
most  of  the  stars  would  be  contained  within  a  limited 
region.  The  clusters  which  we  shall  especially  study 
from  this  point  of  view  are  the  Pleiades,  Coma  Bere- 
nices, Praesepe,  and  Orion. 

The  Pleiades. — In  the  case  of  this  cluster  the  ques- 
tion was  investigated  by  Professor  Bailey,  by  means 
of  a  Harvard  photograph  2°  square,  having  Alcyone 
near  its  centre.  It  was  divided  into  144  squares, 
each  10'  on  a  side.  The  brighter  stars  of  the  cluster 
were  included  within  42  of  these  squares.  The 
count  of  stars  gave  the  results  : 

Within  cluster  :  1012  stars,   or  24  per  square. 
Without  cluster  :  2960  stars,  or  29  per  square. 

It  therefore  seems  that  the  portion  of  the  heavens 
covered  by  the  cluster  is  actually  poorer  in  stars  than 
the  region  around  it. 

Two  opposite  conclusions  might  be  suggested  by 
this  fact.  Assuming  that  the  difference  is  due  to  the 
presence  of  the  cluster,  we  might  suppose  that  the 
latter  was  formed  of  material  that  otherwise  would 
have  gone  into  numerous  smaller  stars.  Accepting 
this  view,  it  would  follow  that  the  material  in  ques- 
tion was  a  sheet  so  thin  that  the  thickness  of  the 


26o  THE  CLUSTERING  OF  THE  STARS 

space  filled  by  the  cluster  was  an  important  fraction 
of  that  occupied  by  the  stars.  In  other  words,  one 
fifth  of  the  stars  of  the  region  would  be  contained  in 
a  thin  sheet.  This  result  seems  too  unlikely  to  be  ac- 
cepted. The  other  and  more  likely  conclusion  is  that 
the  number  of  very  minute  stars  included  in  the  cluster 
is  no  greater  than  that  in  the  surrounding  regions, 
and  that  the  lesser  number  in  the  region  is  to  be 
regarded  as  accidental. 

Coma  Berenices. —  This  cluster,  which  may  be  seen 
east,  south,  or  west  of  the  zenith  on  a  spring  or  summer 
evening,  contains  seven  stars  visible  to  the  naked  eye, 
each  of  the  fifth  magnitude.  It  may  be  considered  as 
comprised  within  the  limits  I2h.  13111.  and  I2h.  25111.  of 
R.  A.,  and  25°  to  29°  of  declination,  an  area  of  io°.5. 
The  existence  of  seven  lucid  stars  within  so  small  an 
area  suggests  that  they  belong  together,  and  may  have 
smaller  stars  belonging  to  the  group,  making  the 
star-density  of  this  area  greater  than  that  of  the  sky 
in  general. 

The  question  whether  there  is  any  corresponding 
excess  of  richness  in  the  fainter  stars  will  be  decided  by 
a  count  of  those  contained  in  Graham's  section  of  the 
A.  G.  Catalogue,  which  extends  to  the  ninth  magni- 
tude. Within  the  area  above  defined  this  catalogue 
gives  71  stars.  Subtracting  the  7  lucid  stars,  we  have 
64  small  stars  left  within  the  area.  To  the  same  belt  of 
declination  336  stars  are  listed  in  the  twelfth  hour  of 
R.  A.,  giving  an  average  of  67  stars  to  an  area  equal 
to  that  of  the  cluster.  The  small  stars  are,  therefore, 
no  thicker  within  the  area  of  the  cluster  than  around 


SMALL  STARS  IN  ORION  261 

it.  It  may  be  added  that  the  seven  lucid  stars  do  not 
seem  to  have  any  common  proper  motion,  so  that 
their  proximity  is  probably  an  accident. 

Prcesepe. — This  object,  situate  in  the  constellation 
Cancer,  appears  to  the  naked  eye  as  a  patch  of 
nebulous  light.  It  is  actually  a  condensed  group  of 
stars,  of  which  the  brightest  are  of  the  seventh  mag- 
nitude. The  stars  of  the  ninth  magnitude  included 
within  the  area  of  the  group  probably  belong,  for  the 
most  part,  to  it,  but  they  are  too  few  to  serve  as  the 
base  for  any  positive  conclusion. 

Orion. — I  find  by  measurement  and  count  that  a 
circle  20°  in  diameter,  comprising  the  brightest  stars 
of  this  constellation,  contains  80  stars  to  magnitude 
6.3.  Of  these,  6  are  of  the  first  or  second,  leaving  74. 
from  the  third  to  the  sixth.  The  resulting  richness 
is  24  to  100  square  degrees,  about  the  average  richness 
along  the  borders  of  the  galaxy.  It  follows  that  this 
remarkable  collection  of  bright  stars  has  no  unusual 
collection  of  faint  stars  associated  with  it. 

A  very  natural  inquiry  is  whether  the  bright  stars 
in  Orion  have  any  common  proper  motion,  indicating 
that  they  form  a  system  by  themselves.  The  answer 
is  shown  in  the  following  statement  of  the  proper 
motions  in  a  century  : 

Proper  Motions. 
Star.  Mag.  R.  A.  Dec.  . 

Rigel i  +0.1  o.o 

tf  Orionis 3  -f~o.  i  — 0.3 

y  Orionis 2  — 0.6  — 1.7 

d  Orionis..              ..2  o.o  — 0.2 


262  THE  CLUSlEiUNG  OF  THE  STARS 

Proper  Motions. 
Star.  Mag.  R.  A.  Dec. 

a  a 

s  Orionis 2                     o.o  4"0-1 

<?  Orion  is 2                     o.o  — 1.4 

K  Orionis 2  -fo.i  — °-3 

a  Orionis. i  +3-°  +0.9 

For  the  most  part  these  motions  are  too  small  to 
be  placed  beyond  doubt,  even  by  all  the  observations 
hitherto  made.  In  the  case  of  Alpha  Orionis  the 
motion  is  established  ;  in  those  of  Gamma  and  Zeta  it 
is  more  or  less  probable,  but  not  at  all  certain  ;  in  all 
the  other  cases  it  is  too  small  to  be  measured. 

This  minuteness  of  the  motion  makes  it  probable 
that  these  stars  are  very  distant  from  us,  an  inference 
which  is  confirmed  by  the  smallness  of  their  parallaxes. 
The  careful  and  long-continued  measures  of  Gill  show 
no  parallax  to  Rigel,  while  Elkin  finds  one  of  only 
o".O2  to  Alpha  Orionis. 

The  general  conclusion  from  our  examination  is 
this  :  The  agglomeration  of  the  brighter  stars  into  clus- 
ters does  not,  in  the  cases  where  it  is  noticeable  to  the 
eye,  extend  to  the  fainter  stars. 

Let  us  now  study  the  question  on  the  opposite  side. 
Schiaparelli's  planispheres  show  regions  of  great  pau- 
city in  lucid  stars  ;  is  there  in  these  regions  any  paucity 
of  telescopic  stars  ? 

The,  two  regions  of  greatest  paucity  are  near  the 
equator  ;  one  extends  through  the  hour  o  of  R.  A.  ; 
the  other  from  i2h.  2om.  to  I2h.  4om.  The  richness 
of  these  and  of  the  adjoining  regions  may  be  inferred 
from  Boss's  zone  of  the  A.  G.  Catalogue,  including  a 


REGIONS  SPARSE  IN  STARS  263 

belt  from  i°  to  5°  of  declination.     The  number  of  stars 
observed  by  Boss  in  each  hour  from  23!}.  to  30.  is  as 

follows  : 

In  23!!.  :  271  stars. 
In  oh.  :  293  stars. 
In  ih.  :  299  stars. 
In  2h.  :  295  stars. 

These  numbers  show  no  paucity  in  the  hour  o,  and 
no  excess  in  the  hour  2,  which  is  much  richer  in  lucid 
stars  than  the  hour  o. 

In  the  strip  from  i2h.  2om.  to  I2h.  4om.  the  cata- 
logue contains  78  stars,  a  richness  of  234  to  the  hour. 
In  the  hour  preceding  there  are  21 1  stars ;  in  that  fol- 
lowing, 225.  There  is,  therefore,  no  paucity  in  the 
strip  in  question. 

We  conclude  from  all  this  that  the  separate  stars  of 
a  cluster  do  not  range  through  a  scale  of  brightness  so 
wide  as  the  stars  in  general,  and  that  they  are  limited 
in  number.  The  numerous  small  stars  seen  in  the 
same  direction  have  no  connection  with  them.  But 
we  shall  see  that  this  rule  does  not  apply  to  the  clus- 
ters of  the  galaxy. 


CHAPTER  XVII 

THE  STRUCTURE  OF  THE  MILKY  WAY 

A  broad  and  ample  road  whose  dust  is  gold, 
And  pavement  stars,  as  stars  to  thee  appear 
Seen  in  the  galaxy,  that  milky  way 
Which  nightly  as  a  circling  zone  thou  seest 
Powdered  with  stars. — MlLTON. 

THE  most  salient  problems  suggested  by  the  ap- 
pearance of  the  Milky  Way  are  to  be  approached 
on  lines  quite  similar  to  those  followed  in  the  last  chap- 
ter. We  begin  with  a  description  of  this  wonderful  ob- 
ject as  it  appears  to  the  observer.  It  can  be  seen 
through  some  part  of  its  course  at  some  hour  on  any 
clear  night  of  the  year,  and  in  the  evening  of  any 
season  except  that  of  early  summer.  In  consequence 
of  its  obliquity  to  the  equator,  its  apparent  posi- 
tion on  the  celestial  sphere,  as  seen  in  our  latitude, 
goes  through  a  daily  change  with  the  diurnal 
rotation  of  the  earth.  In  the  language  of  technical 
astronomy,  every  day  at  i2h.  of  sidereal  time,  it 
makes  so  small  an  angle  with  the  horizon  as  to  be 
scarcely  visible.  If  the  air  is  very  clear,  we  might 
see  a  portion  of  it  skirting  the  northern  horizon. 
This  position  occurs  during  the  evenings  of  early 
264 


DESCRIPTION  OF  THE  MILKY  WAY         265 

summer.  At  oh.  of  sidereal  time,  which  during 
autumn  and  early  winter  fall  in  the  evening,  it 
passes  nearly  through  our  zenith,  from  east  to 
west,  and  can,  therefore,  then  best  be  seen.  We 
begin  with  the  portion  which  will  be  visible  in  the  late 
summer  or  early  autumn.  We  can  then  trace  its 
course  southward  from  Cassiopeia  in  the  northwest. 
It  passes  a  little  east  of  the  zenith  down  to  Sagittarius, 
near  the  south  horizon.  This  portion  of  the  belt  is 
remarkable  for  its  diversity  of  structure  and  the  in- 
tensity of  the  brighter  regions. 

In  Cassiopeia  it  shows  nothing  remarkable  ;  but 
above  this  constellation,  in  Cepheus,  we  notice  in  the 
midst  of  the  brighter  region  a  nearly  circular  and 
comparatively  dark  patch  several  degrees  in  di- 
ameter. A  little  farther  along  we  notice  a  similar 
elongated  patch  in  Cygnus  lying  across  the  course  of 
the  belt.  In  this  region  the  brighter  portions  are  of 
great  breadth,  more  than  20°. 

In  Cygnus  begins  the  most  remarkable  feature  of 
the  Milky  Way,  the  great  bifurcation.  Faintly  visi- 
ble near  the  zenith,  as  we  trace  it  towards  the  south, 
we  see  it  grow  more  and  more  distinct,  until  we  reach 
the  constellation  Aquila,  near  the  equator.  Between 
Cygnus  and  Aquila  the  western  branch  seems  to  be 
the  brighter  and  better  marked  of  the  two,  and  might, 
therefore,  be  taken  for  the  main  branch.  About 
Aquila  the  two  appear  equal,  but  south  of  this  con- 
stellation we  see  the  western  branch  diverge  yet 
farther  toward  the  west,  leaving  the  gap  between  it 
and  the  eastern  vet  broader  and  more  distinct  than 


266      THE  STRUCTURE  OF  THE  MILKY  WAY 

before.  This  branch  finally  terminates  in  the  constel- 
lation Ophiuchus,  while  the  eastern  branch,  growing 
narrower,  can  still  be  followed  toward  the  south. 

Between  the  equator  and  the  southern  horizon  we 
have  the  brightest  and  most  irregular  regions  of  all. 
Several  round,  bright  patches  of  greater  or  less  in- 
tensity are  projected  on  a  background  sometimes 
moderately  bright  and  sometimes  quite  dark.  If  the 
night  is  quite  clear  and  moonless  we  shall  see  that, 
after  a  vacant  stretch,  the  western  branch  seems  to 
recommence  just  about  the  constellation  Scorpius. 
In  this  constellation  we  have  again  a  bifurcation,  a 
dark  region  between  two  bright  ones. 

This  is  about  as  far  as  the  object  can  be  well  traced 
in  our  middle  latitudes.  From  a  point  of  view  nearer 
to  the  equator  it  can  be  traced  through  its  whole  ex- 
tent. South  of  Scorpius  and  Sagittarius  it  becomes 
broad,  faint,  and  diffused  through  the  constellations  of 
Norma  and  Circinus.  It  reaches  its  farthest  south- 
ern limit  in  the  Southern  Cross,  where  it  becomes 
narrower  and  better  defined.  The  most  remarkable 
feature  here  is  the  "  coal  sack,"  a  dark  opening  of 
elliptical  shape  in  the  central  line  of  the  stream. 
West  and  north  of  this,  in  the  constellation  Argo,  is 
the  broadest  and  most  diffused  part  of  the  whole 
stream,  the  breadth  reaching  fully  30°.  Here  we  again 
reach  the  portion  which  rises  above  our  horizon. 

Returning  now  to  our  starting-point,  we  shall 
notice  that,  as  we  make  our  observations  later  and 
later  in  the  autumn,  the  southern  part,  which  we  have 
been  mostly  studying,  is  seen  night  by  night  lower 


TUB  STRUCTURE  OF  THE  MILKY  WAY     267 

down  in  the  west,  while  new  regions  are  coming  into 
view  in  the  north-east  and  east.  These  regions  rise 
earlier  every  evening,  and,  if  we  continue  our  ob- 
servations to  a  later  hour,  we  shall  see  more  and 
more  of  them  above  the  eastern  or  south-eastern 
horizon.  By  midwinter  Cassiopeia  will  be  seen  in 
the  north-west,  and  we  can  readily  trace  the  course  of 
the  galaxy  from  that  constellation  in  the  opposite 
direction  from  that  which  we  have  been  following. 
South  of  Cassiopeia  we  see,  near  the  central  line,  the 
Avell-known  cluster  forming  the  sword-handle  of 
Perseus.  Farther  south  the  belt  grows  narrower  and 
fainter ;  although  the  irregularities  of  structure  con- 
tinue, they  are  far  less  striking  than  on  the  other 
side.  On  a  moonlight  evening  it  will  scarcely  be 
visible  at  all.  If  the  moon  is  absent  and  the  air  clear 
we  shall  see  that  it  grows  slightly  brighter  toward  the 
southern  horizon,  near  which  will  be  the  narrowest 
part  of  its  entire  course.  Below  is  the  broad  and 
diffused  region  in  Argo  already  mentioned. 

One  conclusion  from  the  inequalities  of  structure 
which  we  have  described  will  be  quite  obvious.  The 
Milky  Way  is  something  more  than  the  result  of  the 
general  tendency  of  the  stars  to  increase  in  number 
as  we  approach  its  central  line.  There  must  be  large 
local  aggregations  of  stars,  because,  as  we  have  al- 
ready pointed  out,  there  cannot  be  such  diversity  pf 
structure  shown  in  a  view  of  a  very  widely  stretched 
stratum  of  stars. 

When,  instead  of  a  naked-eye  view  of  the  belt,  we 
study  the  photographs  of  the  Milky  Way,  we  find 


PHOTOGRAPH  SHOWING  STRUCTURE  OF  THE  MILKY  WAY,  BY  BARNARD. 
268 


THE  STRUCTURE  OF  THE  MILKY  WAY     269 

this  evidence  of  clustering  to  grow  still  stronger.  It 
is  seen  very  strikingly  in  the  photograph  by  Bar- 
nard showing  the  singular  rifts  in  the  Milky  Way  in 
the  constellation  Ophiuchus.  Yet  more  singular  are 
three  small  openings  very  close  together  in  the  con- 
stellation Aquila,  the  positions  of  which  are  : 

(1)  R.  A.  =  igh.  35.0111.;  Dec.  =  +  10°  17'. 

(2)  "      =  iph.  36.5111.;  =  +  10°  37'. 

(3)  =  1911.37.201.;  =  +  11°    2'. 

The  fundamental  question  which  we  meet  in  our 
further  study  of  this  subject  is  :  At  what  magnitude 
do  these  agglomerations  of  stars  begin  ?  Admitting, 
as  we  must,  that  they  are  local,  are  they  composed 
altogether  of  faint  stars,  or  do  they  also  include 
the  brighter  stars  within  their  limits  ?  We  consider 
this  question  in  a  way  quite  similar  to  that  in  which 
we  discussed  the  clustering  of  the  stars  in  the  last 
chapter.  We  mark  out  on  a  map  of  the  Milky 
Way  the  brightest  regions — that  is,  those  which 
include  the  densest  agglomeration  of  very  faint  stars. 
We  also  mark  out  the  darkest  regions,  including 
the  coal  sack.  For  this  purpose  I  have  taken  the 
maps  found  in  Heis's  Atlas  Coelestis  for  the  northern 
portion  of  the  Milky  Way  and  the  Atlas  of  Gould's 
Uranometria  Argentina  for  the  southern  portion.  In 
order  to  enable  anyone  to  repeat  and  verify  the  work 
I  give  the  position  of  the  central  part  of  each  patch 
or  region  studied.  This  serves  simply  for  the  pur- 
pose of  indentification.  The  outlines  can  be  drawn 
by  anyone  when  the  patch  is  identified.  In  the 


RIFTS  IN  THE  MILKY  WAY,  PHOTOGRAPHED  BY  BARNARD. 
270 


LUCID  STARS  IN  MILKY  WAY  271 

third  column  of  the  table  is  given,  approximately,  the 
number  of  square  degrees  in  the  patch  as  outlined. 
Then  follows  the  number  of  stars  found  on  the  map. 
Here  are  included  stars  somewhat  fainter  than  those 
regarded  as  lucid.  Heis  maps  all  stars  down  to  about 
magnitude  6.2  or  6.3.  Gould  gives  the  places  of  all 
stars  to  magnitude  7. 

A. — Number  of  lucid  stars  in  certain  bright  regions  or  patches  of 
the  Milky  Way. 

I. — Northern  portion,  from  Heis. 

Number 

of  stars. 

21 

ii 

n 

4 

9 

16 

7 


91 


Stars. 

14 

7 

19 
ii 
7 
9 
5 
5 

Sums  .............     97  77 


Position  of  p 

>atch. 

Area. 

R.A. 

Dec. 

sq.  deg. 

igh.  lorn. 

+  35° 

60 

2oh.    om. 

+  37° 

25 

2oh.  2om. 

+  47° 

20 

2ih.    5111. 

+  45° 

12 

oh.  2om. 

+  60° 

25 

2h.  2om. 

+  55° 

60 

311.  30^' 

+  36° 

32 

3n.  4om« 

+  44° 

43 

Sums 

.    277 

II.  —  Southern  portion 

,  from 

Gould  : 

Position. 

Area. 

R.  A. 

Dec. 

sq.  deg. 

8h.    4m. 

-47° 

10 

2h.  24m. 

-44° 

9 

loh.  35m. 

-58° 

12 

nh.  4om. 

—  62° 

10 

i6h.  lom. 

-53° 

7 

i8h.    om. 

—  28° 

25 

i8h.  torn. 

—  18° 

8 

i8h.  42m. 

—   8° 

16 

272        THE  STRUCTU.RE  OF  THE  MILKY  WAY 

B. — Number  of  lucid  stars  in  the  darker  regions  or  patches  of  the 
Milky  Way. 

I. — Northern  part,  from  Heis. 


Stars. 
10 

7 

12. 
10 
19 
13 
17 

9 
97 


Stars. 
8 
5 
4 
16 
6 
5 

2 

3 
3 

7 


74 
1 A  long  narrow  region  between  the  limits  defined  in  the  first  two  columns. 


Position. 

Area. 

R.  A. 

Dec. 

sq.  deg. 

2ih.    om. 

+  5°° 

26 

22h.    om. 

+  67° 

33 

22h.  25m. 

-j-  60° 

3° 

oh.    om. 

+  69° 

56 

4h.    om. 

+  55° 

98 

4h.  2om. 

+  35° 

98 

6h.  i5m. 

+  18° 

86 

6h.  1  2m. 

+    4° 

48 

Sums 

47"? 

II.  —  Southern  part,  from  Gould. 

Position. 

Area. 

R.  A. 

Dec. 

sq.  deg. 

yh.  22m. 

-38° 

18 

7h.  28m. 

-38° 

12 

8h.    om. 

—  22° 

II 

8h.  40111. 

-50° 

3° 

gh.     om. 

-45° 

12 

loh.     om. 

-52° 

II 

i2h.  4om. 

-63° 

18 

I5h.  lorn. 

-56° 

31 

i7h.  3om. 

-27° 

18 

i8h.  lom. 

-35° 

18 

i8h.     om. 

—  22°) 

i8h.  3om. 

-  14 

24  ' 

i8h.  5om. 

-   5° 

16 

Sums..                     .   210 

LUCID  STARS  IN  MILKY  WAY  273 

To  derive  the  best  conclusions  from  these  numbers 
we  must  compare  them  with  the  mean  star-density 
for  the  sky  in  general,  and  for  the  regions  near  the 
galactic  plane.  Heis  has  3903  stars  north  of  the 
•equator;  Gould,  6755  south  of  it.  The  area  of  each 
hemisphere  is  20,626  square  degrees.  It  will  be  con- 
venient to  express  the  various  star-densities  in  terms 
of  loo  square  degrees  as  the  unit  of  area.  Thus  we 
have  the  following  star-densities  according  to  the  two 
authorities  : 

His.        Gould. 

Star-density  of  the  entire  hemisphere  19.0 32.7 

Star-density  of  the  darker  galactic  regions 20.4 33.8 

Star-density  of  the  bright  galactic  regions 32-9 79-4 

The  first  two  pairs  of  numbers  lead  to  the  remark- 
able and  unexpected  conclusion  that  the  darker  re- 
gions of  the  Milky  Way  are  but  slightly  richer  in 
lucid  stars  than  the  average  of  the  whole  sky ;  cer- 
tainly no  richer  than  is  due  to  the  general  tendency 
of  all  the  stars  to  crowd  toward  the  galactic  plane. 
On  the  other  hand,  the  bright  areas  are  60  per  cent, 
richer  according  to  Heis,  and  more  than  100  per 
cent,  richer  according  to  Gould,  than  the  darker 
areas  seen  among  and  around  them.  The  conclusion 
is  that  an  important  fraction  of  the  lucid  stars  which 
we  see  in  the  same  areas  with  the  agglomerations  of 
the  Milky  Way  is  really  in  those  agglomerations  and 
form  part  of  them. 

A  study  quite  similar  to  this  has  been  made  by 
Easton  for  the  portions  of  the  Milky  Way  between 
Cygnus  and  Aquila.  where  the  diversities  of  brightness 


274        THE  STRUCTURE  OF  THE  MILKY  WAY 

are  greatest.  His  count  of  the  stars  in  the  bright 
and  dark  regions  differs  from  that  made  above 
principally  by  including  all  the  stars  of  the  Durch- 
musterung,  which  we  may  suppose  to  extend  to- 
about  the  ninth  magnitude.1 

He  divides  the  regions  studied  into  six  degrees  of 
brightness.  For  our  present  purpose  it  is  only  ne- 
cessary to  consider  three  regions,  the  brightest,  the 
faintest,  and  those  intermediate  between  the  two. 
Besides  the  count  from  the  Durchmusterung  he  made 
a  count  of  the  same  sort  from  Dr.  Wolf's  photo- 
graphs and  from  Herschel's  gauges  of  the  heavens. 
In  the  following  table  I  have  reduced  all  his  results 
so  as  to  express  the  number  of  stars  in  a  square 
degree  in  the  three  separate  regions.  At  the  top  of 
each  column  is  given  the  authority,  whether  Arge- 
lander,  Wolf,  or  Herschel.  Wolf  had  two  sets  of 
photographs,  one  supposed  to  include  all  the  stars  to- 
the  eleventh,  the  other  to  the  twelfth  magnitude. 
The  magnitudes  included  are  given  in  the  second 
line.  That  Herschel's  count  extends  to  the  fifteenth 
magnitude  is  by  no  means  certain  ;  but  we  can  judge 
from  the  great  number  of  his  stars  that  it  goes  con- 
siderably beyond  Wolf's  in  the  faintness  of  the  stars 
included.  Below  this  we  give,  in  the  regions  A,  B, 
and  C,  which  are  respectively  those  of  least,  of 
medium,  and  of  greatest  brightness,  the  number  of 
stars  per  square  degree  according  to  each  of  the 
authorities  : 

1  Easton's  work  is  given  in  detail  in  the  Astronomische  Nachrichten,  vol. 
137,  and  the  Astrophysical  Journal,  vol.  i,  no.  3. 


STAKS  IN  THE  MILKY  WAY  275 

Authority Arg.  Wolf(A)  Wolf(B)  Herschel. 

Magnitude i — 9  i — n  i — 12  i — 15(7) 

Region  A 23  72  224                405 

Region  B 33  134  764              4114 

Region  C 48  217  1266               6920 

C— A 25  145  1042               6425 

Ratio  C  :  A 2.1  3.0  5.7               14.0 

The  vastly  greater  number  of  individual  stars  per 
square  degree  in  the  brighter  regions  is  what  we 
should  expect  from  the  studies  we  have  made  of  the 
lucid  stars.  But  what  is  of  most  interest  in  the  table 
is  the  continual  increase  in  the  proportion  of  faint 
stars  in  the  separate  regions.  We  notice  that,  when 
we  consider  only  the  stars  of  the  ninth  magnitude^ 
there  are  twice  as  many  in  the  brightest  as  in  the 
darkest  portions.  When  we  go  to  the  eleventh  mag- 
nitude, as  shown  by  Wolf's  photograph  A,  we  find 
the  number  of  stars  in  the  brighter  regions  to  be 
threefold.  When  the  twelfth  magnitude  is  included 
we  find  that  there  are  between  five  and  six  times  as 
many  stars  in  the  bright  regions  as  the  dark  ones. 
Finally,  when  we  come  to  stars  from  Herschel's 
gauges  there  are  fourteen  times  as  many  stars  per 
square  degree  in  the  brighter  regions  as  in  the  dark. 

At  first  sight  this  result  seems  to  show  a  great  dif- 
ference between  the  clusters  of  stars  described  in  the 
last  chapter,  and  the  collections  of  the  Milky  Way, 
in  that  the  former  include  few  or  no  faint  stars,  while 
the  latter  include  a  greater  and  greater  number  as 
we  ascend  in  the  scale  of  magnitude.  This  difference 
is  important  as  showing  a  vastly  greater  range  of  act- 
ual brightness  among  the  galactic  stars  than  among 


276        THE  STRUCTURE  OF  THE  MILKY  WAY 

those  which  form  the  scattered  clusters.  Allowing 
for  this  difference,  the  results  from  the  two  classes 
of  objects  can  be  brought  to  converge  harmoniously 
toward  the  same  conclusion. 

We  have  collected  abundant  evidence  that,  separate 
from  the  accumulations  of  stars  in  the  Milky  Way,  per- 
haps extending  beyond  them,  there  is  a  vast  collec- 
tion of  scattered  stars,  spread  out  in  the  direction  of 
the  galactic  plane,  as  already  described,  which  fill  the 
celestial  spaces  in  every  direction.  We  have  shown 
that  when,  from  any  one  area  of  the  sky,  we  abstract  the 
stars  contained  in  clusters,  this  great  mass  is  not  seri- 
ously diminished.  We  have  also  collected  abundant 
evidence  that  the  distances  of  this  great  mass  are  very 
unequal  ;  in  other  words,  there  is  no  great  accumula- 
tion, in  a  superficial  layer,  at  some  one  distance.  The 
question  which  now  arises  is  whether  the  darker  areas 
which  we  see  in  the  Milky  Way  are  vacancies  in  this 
mass.  Although  some  of  the  counts  seem  to  show 
that  they  are,  yet  a  general  comparison  leads  to  the 
contrary  conclusion.  In  the  darkest  areas  of  the 
Milky  Way,  when  of  great  extent,  the  stars  are  as 
numerous  as  on  each  side  of  the  galactic  zone.  Our 
general  conclusion  is  this  : 

If  we  should  remove  from  the  sky  all  the  local  aggre- 
gations of  stars,  and  also  the  entire  collection  which 
forms  the  cloud-forms  of  the  Milky  Way,  we  should 
have  left  a  scattered  collection,  constantly  increasing  in 
density  toward  the  galactic  belt. 


CHAPTER  XVIII 

THE  PROGRESSION  IN  THE  NUMBER  OF  STARS 
AS  THE  BRIGHTNESS  DIMINISHES 

Hither,  as  to  their  fountain,  other  stars 

Repairing,  in  their  golden  urns  draw  light. — MlLTON. 

WE  mentioned  in  an  earlier  chapter  that,  when 
we  compare  the  number  of  stars  of  each  suc- 
cessive order  of  magnitude  with  the  number  of  the 
order  next  lower,  we  find  it  to  be,  in  a  general  way, 
between  three  and  four  times  as  great.  The  ratio  in 
question  is  so  important  that  a  special  name  must  be 
devised  for  it.  For  want  of  a  better  term,  we  shall 
call  it  the  star-ratio.  It  may  easily  be  shown  that 
there  must  be  some  limit  of  magnitude  at  which  the 
ratio  falls  off.  For  a  remarkable  conclusion  from 
the  observed  ratio  for  the  stars  of  the  lower  order  of 
magnitude  is  that  the  totality  of  light  received  from 
each  successive  order  goes  on  increasing.  Photo- 
metric measures  show,  as  we  have  seen,  that  a  star  of 
magnitude  m  gives  very  nearly  2.5  times  as  much 
light  as  one  of  magnitude  m-\-i.  The  number  of 
stars  of  magnitude  m-{-i  being,  approximately  from 
3  to  3-75  times  as  great  as  those  of  magnitude  m,  it 
follows  that  the  total  amount  of  light  which  they  give 
277 


278      PROGRESSION  IN  NUMBER  OF  STARS 

us  is  some  40  or  50  per  cent,  greater  than  that  re- 
ceived from  magnitude  m.  Using  only  rough  ap- 
proximations, the  amount  of  light  will  be  about 
doubled  by  a  change  of  two  units  of  magnitude  ;  thus 
the  totality  of  stars  of  the  sixth  magnitude  gives 
twice  as  much  light  as  that  of  the  fourth  ;  that  of  the 
eighth  twice  as  much  light  as  that  of  the  sixth  ;  that 
of  the  tenth  twice  as  much  again  as  of  the  eighth, 
and  so  on  as  far  as  accurate  observations  and  counts 
have  been  made. 

To  give  numerical  precision  to  this  result,  let  us 
take  as  unity  the  total  amount  of  light  received  from 
the  stars  of  the  first  magnitude.  The  sum-total  for  this 
and  the  other  magnitudes,  up  to  the  tenth,  will  then  be  : 

Mag.   i Light  =      i.o 

"      - "  -  14 

"      3 "  =  2.0 

"      4 "  =  2.8 

"      5 "  =  4-0 

"      6 «  =  5.7 

"      7 "  =  8.0 

"      8 "  =  11.3 

"      9 "  =  1 6.0 

"    10 "  =  22.6 

Total 74.8 

That  is,  from  all  the  stars  to  the  tenth  magnitude 
combined,  we  have  more  than  seventy  times  as  much 
light  as  from  those  of  the  first  magnitude. 

There  must,  evidently,  be  an  end  to  this  series,  for, 
were  this  not  the  case,  the  result  would  be  that 
which  we  have  shown  to  follow  if  the  universe  were 


PROGRESSION  IN  NUMBER  OF  STARS       279 

infinite  ;  the  whole  heaven  would  shine  with  a  blaze 
of  light  like  the  sun.  At  what  point  does  the  rate  of 
increase  begin  to  fall  off? 

We  are  as  yet  unable  to  answer  this  question,  be- 
cause we  have  nothing  like  an  accurate  count  of  stars 
above  the  ninth,  or  at  most,  the  tenth  magnitude. 
All  we  can  do  is  to  examine  the  data  which  we  have 
and  see  what  evidence  can  be  found  from  them  of  a 
diminution  of  the  ratio. 

It  must  be  pointed  out,  at  the  outset,  that  the  ratio 
must  be  greater  in  the  galactic  region  than  it  is  in 
other  regions.  This  follows  from  the  fact  that  the 
proportion  of  small  stars  increases  at  a  more  rapid 
rate  in  the  galaxy  than  elsewhere.  This  is  shown  by 
the  comparisons  we  have  already  made  of  the  Hersch- 
elian  gauges  with  the  counts  of  the  brighter  stars. 
While  the  galactic  region  is  less  than  twice  as 
dense  as  the  remaining  regions  for  the  brighter  stars, 
it  seems  to  be  ten  times  as  dense  for  the  Herschelian 
stars.  If  we  knew  the  limiting  magnitude  of  the 
latter,  we  could  at  once  draw  some  numerical  conclu- 
sion. But  unfortunately  this  is  quite  unknown.  All 
we  know  is  that  they  were  the  smallest  stars  that 
Herschel  could  see  with  his  telescope. 

The  ratio  in  various  regions  of  the  heavens  has 
been  very  exhaustively  investigated  by  Seeliger,  in 
the  work  already  quoted.  The  bases  of  his  inves- 
tigations are  the  counts  of  stars  in  the  Durchmus- 
terung.  Instead  of  taking  the  ratio  for  stars  differing 
by  units  of  magnitude,  as  we  have  done,  Seeliger 
divides  them  according  to  half-magnitudes.  The 


28o        PROGRESSION  IN  NUMBER  OF  STARS 

reproduction  of  his  numbers  in  detail  would  take 
more  space  than  we  can  here  devote  to  the  subject 
and  would  not  be  of  special  interest  to  our  readers. 
I  have,  therefore,  derived  their  general  mean  results 
for  different  parts  of  the  sky  with  reference  to  the 
Milky  Way  and  for  stars  of  the  various  orders 
of  magnitude.  The  following  table  shows  the  con- 
clusions : 


Ratio  of 

Concluded 

Zone. 

increase. 

result. 

D.  M. 

S.  D. 

Diff. 

I. 

2.99 

— 

— 

3-24 

II. 

3.00 

3-49 

0.49 

3-25 

III. 

3-07 

3-72 

0.65 

3-37 

IV. 

3-32 

3.85 

o-53 

3.58 

V. 

3-55 

4.15 

0.60 

3.85 

VI. 

3.28 

3.68 

0.40 

3-48 

VII. 

3.23 

3-55 

0.32 

337 

VIII. 

3-44 

3-56 

0.12 

3-4° 

IX. 

— 

3-49 



3-24 

In  the  first  column  we  have  the  designation  of  the 
zone  or  region  of  the  sky,  as  already  given. 

In  the  second  and  third  columns  we  have  the  mean 
ratio  of  increase  for  whole  magnitudes  as  derived 
from  the  Durchmusterung  and  the  Southern  Durck- 
musterung,  respectively.  It  will  be  recalled  that 
region  I.,  around  the  north  galactic  pole,  is  entirely 
wanting  in  the  S.  D.,  while  the  adjoining  regions, 
II.  and  III.,  are  only  partially  found,  and  that,  in 
like  manner,  the  D.  M.  includes  none  of  region  IX. 
around  the  south  galactic  pole,  and  but  little  of  the 
adjoining  region. 


SEELIGERS  COUNTS  OF  STARS  281 

It  will  be  seen  that  there  is  a  very  remarkable 
systematic  difference  between  the  two  lists,  the  ratio 
of  the  number  of  faint  to  that  of  bright  stars  being 
much  greater  in  the  S.  D.  This  difference  is  shown 
in  the  fourth  column.  I  have  assumed  that  the  two 
systems  are  equally  good,  and  so  diminished  all  the 
ratios  of  the  S.  D.  by  0.25,  and  increased  those  of 
the  D.  M.  by  the  same  amount.  The  mean  of  the 
two  corrected  results  was  then  taken,  giving  the 
principal  weight  to  the  one  or  the  other,  according 
to  the  number  of  stars  on  which  they  depend. 

It  will  be  seen  that  the  increase  of  the  ratio  from 
either  galactic  pole  to  the  Milky  Way  itself  is  as 
well  marked  as  the  increase  of  the  richness  of  the 
respective  regions  in  stars  in  general.  We  may  con- 
dense the  results  in  this  way  : 

In  the  galactic  zone,  ratio  =  3.85 

In  zones  IV.  and  VI.,  =  3.53 

In  polar  zones  I.,  II.,  VIII.,  and  IX.,  "     =  3.28 

It  will  be  recalled  that  zone  V.  is  a  central  belt  20° 
broad,  including  the  Milky  Way  in  its  limits.  But 
the  latter,  as  seen  by  the  eye,  especially  its  brightest 
portions,  does  not  fill  this  zone.  These  portions,  as 
we  know,  comprise  the  irregular  collection  of  cloud- 
like  masses  described  in  the  last  chapter.  Seeliger 
has  investigated  the  ratio  within  these  masses,  and 
compared  it  with  the  stellar  density,  or  the  number 
of  stars  per  square  degree.  The  mean  results  are  : 

In  that  portion  of  the  galaxy  extending  from  Cas- 
siopeia to  the  equator  near  6h.  of  R.  A.,  ratio  =  4.02. 


282       PROGRESSION  OF  NUMBER  OF  STARS 

In  that  portion  from  Cassiopeia  in  the  opposite 
direction  to  near  igh.  of  R.  A.,  in  Aquila,  ratio  =  3.70. 

These  remarkable  results  are  derived  from  the 
D.  M.,  and  will  be  yet  more  striking  if  corrected  by 
half  the  difference  between  it  and  the  S.  D.,  as  we 
have  done  for  the  sky  generally.  They  will  then  be 
4.27  and  3.95,  respectively. 

As  might  be  expected,  the  regions  of  greater  star 
density  have  generally,  though  not  always,  the  higher 
ratio.  The  highest  of  all  is  in  a  patch  south  of 
Gemini,  between  6h.  and  7h.  of  R.  A.,  and  near  +  5°  of 
declination.  Here  it  amounts  to  5.94,  showing  that 
there  are  eighty-six  stars  of  magnitude  9.0  to  every 
one  of  magnitude  6.5. 

The  D.  M.  does  not  stop  at  magnitude  9,  as  the 
above  numbers  do,  but  extends  to  9.4,  .while  the 
S.  D.  extends  to  magnitude  10.  For  these  magni- 
tudes Seeliger  finds  a  yet  higher  ratio.  This  is, 
however,  to  be  attributed  to  the  personal  equation  of 
the  observers,  and  need  not  be  further  considered. 

The  only  available  material  for  estimating  the 
ratio  of  increase  above  the  ninth  magnitude  is  found 
in  the  Potsdam  photographs  for  the  international 
chart  of  the  heavens,  which  extend  to  magnitude  n. 
These  are  published  only  for  a  few  special  regions. 
Five  of  the  published  plates  fall  in  regions  not  far 
from  the  galactic  pole.  I  have  made  a  count  by 
magnitudes  of  the  312  stars  contained  in  these  plates. 
An  adjustment  is,  however,  necessary  from  the  fact 
that  the  minuter  fractions  of  a  magnitude  could 
not  be  precisely  determined  from  the  photographed 


TOTAL  LIGHT  OF  THE  STARS  283 

images.  The  results  are  practically  given  to  fourths 
of  a  magnitude,  although  expressed  in  tenths.  But 
it  is  found  that  the  numbers  corresponding  to  round 
magnitudes  and  their  halves  are  disproportionately 
more  frequent  than  those  corresponding  to  the  inter- 
mediate fourths.  For  example,  there  are  only  19 
stars  of  magnitude  10.7  and  10.8  taken  together; 
while  there  are  49  of  10.5.  Under  these  circum- 
stances I  have  made  an  adjustment  to  half-mag- 
nitudes by  taking  the  stars  of  quarter-magnitudes 
and  dividing  them  between  half-magnitudes  next 
higher  and  next  lower.  The  number  of  stars  of  the 
several  magnitudes  is  then  as  follows  : 

Mag.  Stars. 

.         6.5 

7.0  2 

7-5  4 

8.0  ii 

8-5  15 

9.0  29 

9-5  33 

10.0  39 

10.5  64 

n.o  115 

It  is  difficult  to  derive  a  precise  value  of  the  star- 
ratio  from  this  table,  owing  to  the  small  number  of 
stars  of  the  brighter  magnitudes,  which  are  insuffi- 
cient to  form  the  first  term  of  the  ratio.  Assuming, 
however,  that  the  ratio  is  otherwise  satisfactorily  de- 
termined up  to  the  ninth  magnitude,  we  find  that 
there  is  but  a  slight  increase  from  the  ninth  up  to  the 
tenth.  The  number  of  the  eleventh  magnitude  is, 


284       PROGRESSION  IN  NUMBER  OF  STARS 

however,  nearly  three  times  that  of  the  tenth  and 
nearly  double  that  of  10.5. 

Another  way  to  consider  the  subject  is  to  compare 
the  total  number  of  stars  of  the  fainter  magnitudes 
with  the  number  of  lucid  stars  corresponding,  which, 
in  the  general  average,  will  be  found  in  the  same 
space.  We  may  assume  that  near  the  poles  of  the 
galaxy  there  is  about  one  lucid  star  to  every  ten 
square  degrees.  The  five  belts  included  in  the 
above  statement  cover  about  thirteen  square  degrees. 
The  region  is,  therefore,  that  which  would  contain 
about  one  star  of  the  sixth  magnitude.  An  increase 
of  this  number  by  somewhat  more  than  100  times  in 
the  five  steps  from  the  sixth  magnitude  to  the 
eleventh  would  indicate  a  ratio  somewhat  less  than 
3  ;  about  2.5.  But  the  comparison  of  the  photo- 
graphic and  visual  magnitudes  renders  this  estimate 
somewhat  doubtful.  Besides  this,  it  is  questionable 
whether  we  should  not  reckon  among  stars  of  the 
eleventh  magnitude  those  up  to  11.5,  which  would 
greatly  increase  the  number.  It  is  a  little  uncertain 
whether  we  should  regard  the  limit  of  magnitude  on 
the  Potsdam  plates  as  n.o  or  n  plus  some  fraction 
near  to  one  half. 

Altogether,  our  general  conclusion  must  be  that  up  to 
the  eleventh  magnitude  there  is  no  marked  falling  off  in 
the  ratio  of  increase,  even  near  the  poles  of  the  galaxy. 

I  have  not  made  a  corresponding  count  for  the 
galactic  region,  but  the  great  number  of  stars  given 
on  the  plates  show,  as  we  might  expect,  that  there  is 
no  diminution  in  the  ratio  of  increase. 


TOTAL  LIGHT  OF  THE  STARS  285 

The  question  where  the  series  begins  to  fall  away 
is,  therefore,  still  an  undecided  one,  and  must  remain 
so  until  a  very  exact  count  is  made  of  the  photo- 
graphs taken  for  the  international  photographic  chart 
of  the  heavens,  or  of  the  Harvard  photographs. 

There  is  also  a  possibility  of  applying  a  photometric 
study  of  the  sky  to  the  question.  The  background  of 
the  sky  itself  is  by  no  means  black.  The  question 
to  be  investigated  is  whether  a  considerable  fraction 
of  the  apparently  smooth  and  uniform  light  of  the 
nightly  sky  comes  from  countless  telescopic  stars, 
perhaps  from  stars  too  faint  to  be  found  on  the  most 
delicate  photographs,  or  whether  it  is  mostly  reflected 
by  our  atmosphere  from  the  stars.  It  may  seem 
questionable  whether  the  latter  is  the  case,  because 
the  fraction  reflected  in  a  clear  atmosphere  is  not 
supposed  to  exceed  one  tenth  the  total  amount  of 
light  of  the  stars  themselves.  On  the  other  hand, 
the  seemingly  blue  colour  of  the  sky  might  seem  to 
indicate  reflected  light,  since  the  average  colour  of  all 
the  stars  is  white  rather  than  blue.  The  subject  is 
an  extremely  interesting  one  and  requires  investi- 
gation before  a  definitive  conclusion  can  be  reached. 


CHAPTER  XIX 
STATISTICAL   STUDIES  OF  PROPER  MOTIONS 

How  charming  is  divine  philosophy, 

Not  harsh  and  crabbed  as  dull  fools  suppose, 

But  musical  as  is  Apollo's  lute, 

And  a  perpetual  feast  of  nectared  sweets 

Where  no  crude  surfeit  reigns. — MILTON. 

THE  number  of  stars  now  found  to  have  a  proper 
motion  is  sufficiently  great  to  apply  a  statistical 
method  to  their  study.  The  principal  steps  in  this 
study  have  been  taken  by  Kapteyn,  who,  in  several 
papers  published  during  the  past  ten  years,  has  shown 
how  important  conclusions  may  be  drawn  in  this  way. 
We  must  begin  our  subject  by  showing  the  geo- 
metrical relations  of  the  proper  motion  of  a  star,  con- 
sidered as  an  actuality  in  space,  to  the  proper  motion 
as  we  see  it.  The  motion  in  question  is  supposed  to 
take  place  in  a  straight  line  with  uniform  velocity. 
Leaving  out  the  rare  cases  of  variations  in  the  motion 
due  to  the  attraction  of  a  revolving  body,  there  is 
nothing  either  in  observation  or  theory  to  justify  us 
in  assuming  any  deviation  from  this  law  of  uniformity. 
The  direction  of  a  motion  has  no  relation  to  the  di- 
rection from  the  earth  to  the  star.  That  is  to  say,  it 
may  make  any  angle  whatever  with  that  direction. 
286 


COMPONENTS  OF  PROPER  MOTION         287 

Let  E  be  the  position  of  our  solar  system,  and  S 
that  of  a  star  moving  in  the  direction  of  a  straight 
line,  S  D.  It  must  not  be  understood  that  the  length 
of  this  line  is  taken  to  represent  the  actual  motion  ; 
the  latter  would  be  infinitesimal  as  compared  with  its 
length;  we 
use  it  only  to 
show  direc- 
tion. We 
may,  however,  E 

use  the  line  to  COMpONENTs  OP  PROPER  MOT.ON. 

represent     on 

a  magnified  scale  the  actual  amount  of  the  motion 
during  any  unit  of  time,  say  one  year.  It  may  be 
divided  into  two  components  :  one,  S  R,  in  the  direc- 
tion of  the  line  of  sight  from  us  to  the  star,  which  for 
brevity  we  shall  call  the  radial  line,  and  the  other, 
S  M,  at  right  angles  to  that  line. 

It  must  be  understood  that,  as  the  term  "  proper 
motion  "  is  commonly  used,  only  the  component  S  M 
can  be  referred  to,  because  the  radial  component,  S  R, 
does  not  admit  of  being  determined  by  telescopic 
vision.  As  we  know  from  the  preceding  chapters,  it 
can  in  the  case  of  the  brighter  stars  be  determined 
by  spectroscopic  measurement  of  the  radial  motion. 

The  visible  component,  S  M,  can  also  be  resolved 
into  two  perpendicular  components,  the  one  east  and 
west  on  the  celestial  sphere,  the  other  north  and 
south.  The  former  is  the  proper  motion  in  right 
ascension  (the  measured  motion  in  this  co-ordinate 
being  multiplied  by  the  cosine  of  the  declination 


288    STATISTICAL  STUDIES  OF  PROPER  MOTION 

to  reduce  it  to  a  great  circle),  and  the  other  is  the 
proper  motion.in  declination.  In  star  catalogues  these 
two  motions  are  given,  so  far  as  practicable.  Thus, 
altogether,  the  actual  motion  of  a  star  in  space  may  be 
resolved  into  three  components :  that  of  right  ascen- 
sion, that  of  declination,  and  the  radial  component. 

An  additional  consideration  is  now  to  be  added. 
The  proper  motion  of  a  star,  as  observed  and  given 
in  catalogues,  is  a  motion  relative  to  our  system.  It 
has  been  shown  in  a  former  chapter  that  the  latter 
has  a  proper  motion  of  its  own.  When  account  is 
taken  of  this,  and  the  motions  are  all  reduced  as  well 
as  we  can  to  a  common  centre  of  gravity  of  the  whole 
stellar  system,  we  conceive  the  observed  proper  mo- 
tion of  the  star  to  be  made  up  of  two  parts,  of  which 
one  is  the  actual  motion  of  the  star  relative  to  the 
common  centre,  and  the  other  due  to  the  motion  of 
the  sun,  carrying  the  earth  with  it.  The  direction 
of  the  latter  appears  to  us  opposite  that  of  the  motion 
of  the  sun.  The  sun's  motion  being  directed  to  the 
constellation  Lyra,  it  follows  that  the  component 
in  question  in  the  case  of  the  stars  is  directed  toward 
the  opposite  constellation,  Argo.  This  component, 
as  we  know,  is  termed  the  parallactic  motion,  being 
dependent  on  the  distance  or  parallax  of  the  star. 

As  in  the  case  of  other  proper  motions,  we  may 
measure  the  parallactic  motion  either  in  angular 
measure,  as  so  many  seconds  per  century,  or  in  linear 
measure,  as  so  many  kilometres  per  second.  The  re- 
lation of  the  two  measures  depends  on  the  distance 
of  a  star.  The  simplest  conception  of  the  relation 


PARALLACTIC  MOTION  289 

may  be  gained  by  reflecting  that  the  linear  speed  of 
the  parallactic  motion  must  be  equal  to  that  of  the 
sun. 

We  have  cited  Campbell's  result  for  the  speed  of 
the  solar  motion,  which  is  between  19  and  20  km.  per 
second,  or  4  radii  of  the  earth's  orbit  per  year.  Ac- 
cepting this  speed  we  shall  have  the  following  rule  : 

The  parallax  of  a  star  lying  in  a  direction  nearly  at 
right  angles  to  that  of  the  solar  motion  is  equal  to  one 
fourth  of  its  annual  parallactic  motion. 

In  the  case  of  stars  in  other  directions,  the  paral- 
lactic motion  for  a  given  parallax  would  be  less  in 
proportion  to  the  sine  of  the  angle  between  the  direc- 
tion of  the  star  and  the  solar  apex. 

If  the  stars  were  at  rest  this  rule  would  enable 
us  immediately  to  determine  the  distance  of  any  star 
by  its  proper  motion,  which  would  then  be  simply  the 
parallactic  motion  itself.  Unfortunately,  in  the  case 
of  any  one  star  considered  individually,  there  is  no 
way  of  deciding  how  much  of  its  motion  is  proper  to 
itself  and  how  much  is  the  parallactic  motion.  But 
when  we  consider  the  great  mass  of  stars,  it  is  possible 
in  a  rough  way  to  make  a  distinction  between  the 
two  motions  in  a  general  average. 

The  direction  or  motion  of  any  particular  star, 
having  no  reference  to  that  of  the  sun,  is  as  likely  to 
be  in  the  direction  of  one  of  the  three  components  we 
have  described  as  of  any  other.  Hence,  in  the  aver- 
age of  a  great  number  of  stars  we  may  conclude  that 
these  components  are  equal. 

One  of  the  simplest  applications  of  this  law  will 


290    STATISTICAL  STUDIES  OF  PROPER  MOTION 

enable  us  to  compute  the  mean  parallax  of  the  stars 
whose  radial  motions  have  been  determined.  As 
this  application  is,  in  the  present  connection,  made 
only  for  the  purpose  of  illustration,  I  shall  confine 
myself  to  the  47  stars  of  which  the  radial  motions 
have  been  measured  by  Vogel.  The  mean  annual 
proper  motions  of  these  stars,  taken  without  any  re- 
gard to  their  signs,  are  : 

Including  Arcturus.     Omitting  Arcturus. 

In  right  ascension. ..   0.163  °-I44 

In  declination °-l55  0.118 

The  difference  of  the  mean  motions  in  right  ascen- 
sion and  declination  is  to  be  regarded  as  accidental. 
The  velocity  of  Arcturus  is  so  exceptionally  great 
that  we  ought,  perhaps,  to  leave  it  out  in  taking  the 
mean. 

Now,  the  mean  of  the  radial  motions  as  found  by 
Vogel  is  1 6  kilometres  per  second.  By  hypothesis 
the  actual  motion  in  the  radial  line  is  in  the  general 
average  the  same  as  in  the  other  two  directions. 
We  have,  therefore,  to  determine  what  must  be  the 
parallax  of  a  star  in  order  that,  moving  with  a  veloc- 
ity of  1 6  kilometres  per  second,  its  angular  proper 
motion  may  have  one  of  the  above  values.  This 
result  is  by  a  simple  computation  found  to  be  : 

From  the  mean  motion  in  R.  A. 0.049  or  0.043 

From  the  mean  motion  in  Dec 0.046  or  0.035 

The  difference  of  these  results,  which  depends  oa 


COMPONENTS  OF  PROPER  MOTION         291 

the  omission  or  exclusion  of  Arcturus,  shows  the 
amount  of  uncertainty  of  the  method.  Our  general 
conclusion,  therefore,  is  that  the  mean  parallax  of 
the  Vogel  stars,  which  may  be  regarded  as  corres- 
ponding approximately  to  the  mean  parallax  of  all 
the  stars  of  the  second  magnitude,  is  about  o".o4. 

We  have  spoken  of  the  two  components  of  the 
apparent  motion  as  those  in  right  ascension  and 
declination,  respectively.  But  there  is  no  particular 
significance  in  the  direction  of  these  co-ordinates, 
which  have  no  relation  to  the  heavens  at  large.  For 
some  purposes  it  will  be  better  to  take  as  the  two 
directions  in  which  the  motions  are  to  be  resolved 
that  of  the  parallactic  motion  and  that  at  right  angles 
to  it.  That  is  to  say,  taking  the  solar  apex  as  a  pole, 
we  conceive  an  arc  of  a  great  circle  drawn  upon  the 
celestial  sphere  from  it  to  the  star,  and  resolve  the 
apparent  motion  into  two  components,  the  one  in 
the  direction  of  this  arc,  the  other  at  right  angles  to 
it.  The  former,  which  we  may  call  the  apical  motion, 
is  affected  by  the  parallactic  motion ;  the  latter, 
which  we  call  the  cross  motion,  is  not,  and  therefore 
shows  the  true  component  of  the  motion  of  the  star 
itself  in  the  direction  indicated. 

Kapteyn  has  gone  through  the  labour  of  resolving 
all  the  proper  motions  of  the  Bradley  stars  given  by 
Auwers,  in  this  way.  His  assumed  position  of  the 
solar  apex  was : 

Right  ascension 276°  =  i8h.  2401. 

Declination  ' +34° 

1  This  work    of  Kapteyn  is  unpublished.      The  author  is  indebted  to  his 


292     STATISTICAL  STUDIES  OF  PROPER  MOTION 

The  radically  new  treatment  in  his  discussion  of 
the  distribution  of  the  stars  in  space  embraces  three 
points.  The  first  consists  in  the  distinction  between 
the  spectral  types  of  the  different  stars  and  the  sepa- 
rate study  of  the  proper  motions  peculiar  to  each 
type.  The  next  point  is  the  reference  of  the  motions 
to  the  solar  apex.  The  third  is  the  study  of  the  re- 
lations of  the  stars  to  the  galactic  plane. 

A  remarkable  relation  existing  between  the  spectral 
type  of  stars  and  their  proper  motions l  was  brought 
out  by  these  investigations.  The  stars  of  Type  I. 
have,  in  the  general  mean,  smaller  proper  motions 
than  those  of  Type  II.  The  following  table  is  made 
up  from  Kapteyn's  work.  First  we  give  the  limits 
of  proper  motion  ;  then  on  the  same  line  the  number 
of  stars  of  the  respective  Types  I.  and  II.  having 
proper  motions  within  these  limits  : 

Centennial  Number  of  stars, 

prop,  motions.  Type  1.     Type  II. 

it  n 

o  to  5  786  474 

6  to  9  203  194 

10  to  19  159  223 

20  to  29  25  86 

30  to  49  13  71 

50  and  more  3  58 


Total  1189     1106 

courtesy  for  a  manuscript  copy,  with  permission  to  use  it.  Kapteyn's  re- 
searches based  on  this  material  are  contained  in  a  series  of  papers  communi- 
cated to  the  Amsterdam  Academy  of  Science.  An  abstract  in  English  of  one 
of  the  earlier  papers  is  found  in  Knowledge  for  June  i,  1893. 

1  The  author  believes  that  Monck,  of  England,  independently  pointed  out 
this  relation,  perhaps  in  advance  of  Kapteyn. 


MOTIONS  OF  TWO  SPECTRAL  TYPES        293 

It  will  be  seen  that  in  the  case  of  stars  having 
proper  motions  of  less  than  5"  per  century  a  large 
majority  are  of  Type  I.  In  the  case  of  proper  mo- 
tions between  6"  and  9"  the  number  is  nearly  equal. 
Between  10"  and  20"  there  is  a  large  majority  of 
Type  II.  Between  30"  and  49"  the  number  of  Type 
II.  is  nearly  five  times  that  of  Type  I.  Finally,  only 
three  stars  of  Type  I.  have  proper  motions  exceed- 
ing 50",  while  fifty-eight  stars  of  Type  II.  have  a 
proper  motion  exceeding  this  limit. 

We  may  make  two  hypotheses  on  this  subject : 
one,  that  the  stars  of  Type  II.  really  move  more 
rapidly  than  those  of  Type  I.  ;  the  other,  that  their 
actual  motion  is  the  same,  but  that  the  stars  of  Type 
I.  are  more  distant  stars.  The  last  conclusion  seems 
much  more  probable,  and  is  strengthened  by  the 
much  greater  condensation  of  stars  of  Type  I.  toward 
the  Milky  Way. 

Let  us  now  consider  the  principles  by  which  we 
may  study  a  great  collection  of  proper  motions 
statistically.  There  are  scattered  around  us  in  the 
stellar  spaces,  in  every  direction  from  us,  a  large 
number  of  stars,  each  moving  onward  in  a  straight 
line  and  in  a  direction  which,  with  rare  exceptions, 
has  nothing  in  common  with  the  motion  of  any  other 
star.  The  velocities  of  the  motion  vary  from  one 
star  to  another  in  a  way  that  cannot  be  determined,1 
some  moving  slowly  and  some  rapidly.  Is  it  pos- 
sible from  such  a  maze  of  motions  to  determine  any- 
thing ?  Certainly  we  cannot  learn  all  that  we  wish, 
yet  we  may  learn  something  that  will  help  us  to 


294 


STATISTICAL  STUDIES  OF  PROPER  MOTION 


form  some  idea  of  the  respective  distances  of  the 
stars  and  the  actual  velocity  of  their  motions.  An 
obvious  remark  is  that  the  more  distant  a  star  the 
slower  it  will  seem  to  move.  We  must,  therefore, 
distinguish  between  the  linear  or  actual  motion  of 
a  star,  expressed  as  so  many  kilometres  per  second, 
and  its  apparent  or  angular  motion  of  so  many 
seconds  per  year,  derived  by  measuring  its  change  of 
direction  as  we  see  it  with  our  instruments. 

We  shall  now  endeavour  to  explain  Kapteyn's 
method  in  such  a  way  that  the  reasoning  shall  be  clear 
without  repeating  the  algebraic  operations  which  it 
involves.  Let  us  conceive  that  the  following  Fig.  is 
drawn  on  the 
celestial  sphere  \ 

as  we  look  up 
at  the  heavens. 
S  is  the  direc- 
tion of  a  star  in 
the  sky  as  we 
see  it.  Let  us 
also  suppose 

that  the  solar  apex,  situated  in  the  constellation  Lyra, 
lies  anywhere  horizontally  to  the  left  of  the  star,  in  the 
direction  of  the  arrow-head  marked  Apex.  Suppose 
also  that,  were  the  solar  system  at  rest,  we  should  see 
the  star  moving  along  the  line  S.  D.  Let  the  length  of 
the  line  S  D  represent  the  motion  in  some  unit  of  time, 
say,  one  year.  Next,  suppose  the  star  at  rest.  Then 
in  consequence  of  the  motion  of  the  solar  system,  by 
which  we  are  carried  toward  the  apex,  the  star  would 


APICAL  AND  CROSS  MOTIONS  295 

seem  to  be  moving  with  its  parallactic  motion  in  the 
direction  S  B,  away  from  the  apex.  Let  the  length 
of  this  line  represent  the  parallactic  motion  in  one 
year.  Then  by  the  theory  of  composition  of  mo- 
tions, the  star,  moving  by  its  real  motion  from  S  to  D, 
and  by  the  motion  of  the  earth  having  an  apparent 
motion  from  S  to  B,  will  appear  to  us  to  move  along 
the  diagonal  S  A  of  the  parallelogram.  Thus,  the 
line  S  A  will  represent  the  annual  proper  motion  of 
the  star  as  we  observe  it  with  our  instruments,  and 
which  can  be  resolved  into  the  apical  motion,  in  the 
direction  S  B,  and  its  cross-motion  in  the  direction  S. 

The  apical  motion  consists  of  two  parts,  one  the 
parallactic  motion,  equal  to  S  B  ;  the  other  real,  and 
due  to  the  motion  of  the  star  itself  along  the  line 
S  D,  and  equal  to  the  distance  of  D  from  the  line  S  r. 

We  have  now  to  inquire  how,  in  the  case  of  a  great 
number  of  stars,  we  may  distinguish  between  these 
two  parts  of  the  apical  motion. 

We  must  make  the  general  hypothesis  that,  in  the 
average  of  a  great  number  of  stars,  actual  motions 
have  no  relation  to  the  direction  of  our  sun  from  the 
star.  Then  the  components  of  the  actual  motion, 
S  D,  will  in  the  general  average  have  equal  values, 
positive  and  negative  motions  cancelling  each  other. 
Hence,  if  we  take  the  mean  of  a  great  number  of 
motions  along  the  apical  line  it  will  give  us  the 
value  of  S  B  due  to  the  motion  of  the  earth,  and, 
hence,  the  mean  parallactic  motion  of  all  the  stars 
considered. 

The  problem  now  becomes  one  of  averages.     We 


296    STATISTICAL  STUDIES  OF  PROPER  MOTION 

wish  to  form  at  least  a  rude  estimate  of  the  average 
speed  of  a  star  in  miles  or  kilometres  per  second.  To 
show  how  this  may  be  done  let  us  suppose  that  we 
observe  the  proper  motions  of  a  great  number  of 
stars  at  some  distance  from  the  solar  apex,  so  that 
their  parallactic  motion  shall  be  observable.  Stumpe 
and  Ristenpart,  the  German  astronomers,  as  well  as 
Kapteyn,  have  considered  the  relation  between  the 
two  motions  in  the  following  way  :  We  divide  the 
stars  observed  into  classes,  taking,  say,  one  class  hav- 
ing small  but  easily  measured  proper  motion  ;  another 
having  a  proper  motion  near  the  average,  and  a  third, 
of  large  proper  motion.  Sometimes  a  fourth  class  is 
added,  consisting  of  stars  having  exceptionally  large 
proper  motions.  From  each  of  these  classes  we  can 
determine,  as  already  shown,  the  average  motion 
from  the  direction  of  the  solar  apex ;  that  is  to  say, 
the  average  parallactic  motion.  This  will  be  inversely 
as  the  average  distance  of  the  stars. 

Stumpe's  three  classes  were  :  I.,  proper  motions 
ranging  from  16"  to  32"  per  century;  II.,  between 
32"  and  64"  per  century;  III.,  between  64"  and  128" 
per  century;  IV.,  greater  than  128".  The  average 
of  the  proper  motions  in  each  class,  the  average  of 
the  apparent  apical  motions,  and  the  ratio  of  the  two 
are  these : 

Class.  Prop.  Mot.         Par.  Mot.          Quotient. 

It  If 

I.  0.23  0.142  1.6 

II.  0.43  0.286  1.5 

III.  0.85  0.583  1.4 

IV.  2.39  2.057  i.i 


AVERAGE  SPEED  OF  A  STAR  297 

It  will  be  seen  that  the  ratio  of  the  proper  motion 
of  the  star  to  the  parallactic  motion  diminishes  as  the 
former  increases. 

The  same  thing  was  found  by  Ristenpart  from  the 
proper  motions  of  the  Berlin  zone,  as  shown  below : 
Class.  Prop.  Mot.         Par.  Mot.          Quotient. 

ft  n 

Small  0.128  0.061  2.1 

Medium         o  197  0.109  l-& 

Large  0.374  0.279  i-3 

The  smaller  value  of  the  quotient  from  stars  near 
to  us  than  from  the  more  distant  stars  was  supposed 
to  lead  to  the  conclusion  that  the  latter  had  a  more 
rapid  real  motion  than  the  former.  A  little  thought 
will  show  that,  while  this  is  quite  true  of  the  stars  in- 
cluded in  the  list,  this  does  not  prove  it  to  be  true  for 
the  stars  in  general.  We  cannot,  as  already  pointed 
out,  determine  the  motion  of  any  star  unless  it  ex- 
ceeds a  certain  limit.  Hence,  in  the  case  of  the  more 
distant  stars  we  can  observe  the  proper  motions  only 
of  those  which  move  most  rapidly,  while  in  the  case 
of  the  nearer  ones  we  may  have  measured  them  all. 
We  should,  therefore,  naturally  expect  that  the  more 
distant  stars  in  our  list  will  show  too  large  a  value  of 
the  proper  motion,  for  the  simple  reason  that  those 
having  small  proper  motion  are  not  included  in  the 
average.  There  is,  therefore,  no  evidence  that  the 
more  distant  stars  move  faster  than  the  nearer  ones. 

An  error  in  the  opposite  direction  occurs  through 
the  method  of  selecting  stars  of  given  proper  motion. 
We  have  already  pointed  out  that  in  the  case  of  any 


298    STATISTICAL  STUDIES  OF  PROPER  MOTION 

individual  star  we  cannot  determine  how  much  of  its 
apparent  apical  motion  may  be  that  of  the  star  itself, 
and  how  much  the  parallactic  motion  arising  from 
the  motion  of  the  earth.  What  we  have  done  is  to 
assume  that  in  the  case  of  a  great  number  of  stars 
the  actual  apical  motions  will  be  equal,  and  in  op- 
posite directions,  so  as  to  cancel  each  other  in  the 
average  of  a  great  number,  leaving  this  average  as 
the  parallactic  motion.  Now,  to  fix  the  ideas,  sup- 
pose that  two  stars  have  an  equal  apical  motion,  say 
three  radii  of  the  earth's  orbit  in  a  year,  but  in  opposite 
directions.  The  apical  motion  of  the  earth  being  four 
radii  per  year,  it  follows  that  the  star  which  is  mov- 
ing in  the  same  direction  as  the  earth  will  have  a 
relative  apical  motion  of  only  i,  and  will,  therefore, 
not  appear  in  our  list  as  a  star  of  large  proper  mo- 
tion. On  the  other  hand,  the  star  moving  with  equal 
speed  in  the  opposite  direction  will  have  a  motion  of 
seven  radii  per  year,  and  will,  therefore,  be  included 
among  stars  of  considerable  proper  motion.  Thus,  a 
bias  occurs,  in  consequence  of  which  we  include  many 
stars  having  a  motion  away  from  the  solar  apex,  while 
the  corresponding  ones,  necessary  to  cancel  that  mo- 
tion, will  be  left  out  of  the  count.  Thus,  the  parallactic 
motion  will,  in  the  average,  be  too  large  in  the  case 
of  the  stars  of  large  apparent  proper  motion.  Now, 
this  is  exactly  what  we  see  in  the  above  tables.  As 
we  take  the  classes  with  larger  and  larger  proper 
motions,  the  supposed  parallactic  motion,  which  is 
really  the  mean  of  the  apical  motions,  seems  to  in- 
crease in  a  yet  larger  degree.  It  is,  therefore,  impos- 


AVERAGE  SPEED  OF  A  STAR  299 

sible  to  determine  from  comparisons  like  these  what 
the  exact  ratio  is. 

This  error  is  avoided  when  we  do  not  arrange 
and  select  the  stars  according  to  the  magnitude  of 
their  proper  motions,  but  take  a  large  list  of  stars, 
determine  their  proper  motions  as  best  we  can,  and 
draw  our  conclusions  from  the  whole  mass.  This 
has  been  done  by  Kapteyn  in  the  paper  already 
quoted.  By  a  process  too  intricate  to  be  detailed  in 
the  present  work  he  has  reached  certain  conclusions 
as  to  the  ratio  of  the  actual  motion  of  the  sun  in 
space  to  the  average  motion  of  the  stars.  His  defin- 
itive result  is  : 

Average  speed  of  a  star  in  space 
—  Speed  of  solar  motion  X  1.86. 

This  I  shall  call  the  straight-ahead  motion  of  the 
star,  without  regard  to  its  direction.  But  the  actual 
motion  as  we  see  it  is  the  straight-ahead  motion,  pro- 
jected on  the  celestial  sphere.  The  two  will  be  equal 
only  in  cases  where  there  is  no  radial  motion  to  or 
from  the  earth.  In  all  other  cases  the  motion  which 
we  observe  will  be  less  than  the  straight-ahead  mo- 
tion. By  the  process  of  averaging,  Kapteyn  finds  : 

Linear  projected  speed  of  a  star 
=  Speed  of  solar  motion  X  1.46. 

This  projected  motion,  again,  may  be  resolved  into 
two  components  at  right  angles  to  each  other.  It 
follows  that  the  average  value  of  either  component 
will  be  less  than  that  of  the  projected  motion.  The 
components  may  be  the  motions  in  right  ascension 


300    STATISTICAL  STUDIES  OF  PROPER  MOTION" 

or  declination,  or  the  apical  motion  and  the  motion  at 
right  angles  to  it.  In  any  case,  the  mean  value  of  a 
component  will  be  : 

Speed  of  solar  motion  X  0.93. 

I  have  used  Kapteyn's  numbers  to  obtain  the  same 
relation  by  a  somewhat  different  and  purely  statis- 
tical method. 

Imagine  the  proper  motion  of  a  star  situated  nearly 
at  right  angles  to  the  direction  of  the  solar  motion. 
Although  we  cannot  determine  how  much  of  its 
apical  motion  is  actual  and  how  much  is  parallactic, 
we  can  determine  whether  its  motion,  if  toward  the 
solar  apex,  exceeds  that  of  the  sun.  In  fact,  all  stars 
the  apical  component  of  whose  motion  is  in  the  same 
direction  and  greater  than  that  of  the  sun,  whatever 
the  distance  of  the  star,  appear  to  us  as  moving 
toward  the  apex,  a  direction  to  which  we  assign  a 
negative  algebraic  sign.  All  stars  moving  more 
slowly  than  this,  or  in  the  opposite  direction  from 
the  sun,  will  have  apparent  motions  away  from  the 
apex,  which  we  regard  as  algebraic  ally  positive.  We 
can,  therefore,  by  a  simple  count  separate  the  stars 
moving  in  the  same  direction  as  the  sun,  and  with 
greater  speed,  from  all  the  others. 

I  have  classified  the  stars  in  this  way,  not  only  as  a 
whole,  but  also  with  reference  to  their  cross  motion — 
motion  at  right  angles  to  that  of  the  sun.  That  is  to 
say,  I  have  taken  the  stars  whose  cross  motion,  r, 
is  2"  per  century  or  less  and  counted  their  apical- 
motions  as  positive,  negative,  and  zero.  Then  I  have 


AVERAGE  SPEED  OF  A  STAR 


301 


done  the  same  thing  with  cross  motions  of  3"  or  4", 
then  with  cross  motions  ranging  from  5"  to  7",  and 
so  on.  All  cross  motions  above  13"  we  put  together.1 
The  results  of  this  work  are  shown,  so  far  as  described, 
in  the  first  four  columns  of  the  table  below.  We  have 
here,  for  the  various  values  of  r,  the  number  of  posi- 
tive, negative,  and  zero  apical-motions. 

Table,  showing  the  number  of  positive  and  negative 
apical  motions  for  different  values  of  the  crossmotion. 


Values  of 
r 

Apical  Motions,  6 

Percentage. 

Pos. 

Zero. 

Neg. 

P'. 

N'. 

P. 

N. 

1,013 

360 

285 

215 

216 

261 
56 
.  37 
7 

2 

425 
1  60 
107 

52 
61 

V43 
388 

3°3 
218 
217 

555 
188 

I25 
55 
62 

0.67 
0.67 
0.71 
0.80 
0.78 

°-33 
°-33 
0.29 

O.2O 
0  22 

4-~t    4. 

•  4-  C  to  7  .  . 

-|-  8  to  12   

-4-  n  4- 

Totals  

2,089 

363 

805 

2,269 

985 

0.70 

0.30 

The  first  question  that  arises  in  connection  with  this 
table  is,  how  to  count  the  motions  that  come  out  zero  ; 
that  is  to  say,  those  which  are  too  small  to  be  certainly 
observed.  The  most  probable  distribution  we  can 
make  of  them  is  to  suppose  that  they  are  equally  di- 
vided between  positive  and  negative  motions.  I  have, 
therefore,  added  one-half  of  the  zero  motions  to  the 
positive  and  one-half  to  the  negative  column,  thus 
getting  the  results  given  in  columns  P'  and  N'.  The 


1  The  author  should  say  that  the  greater  part  of  the  work  on  these  countings 
was  done  with  great  care  and  accuracy  by  Mrs.  Arthur  Brown  Davis. 


3o2    STATISTICAL  STUDIES  OF  PROPER  MOTION 

percentages  of  positive  and  negative  motions  thus  re- 
sulting are  given  in  the  last  column. 

We  see  that  there  is  a  fairly  regular  progression  in 
the  percentage,  depending  on  the  value  of  the  cross 
motion.  In  the  case  of  the  small  cross  motions,  which 
presumably  belong  to  the  more  distant  stars,  the  per- 
centage of  negative  apical  motions  is  markedly  greater 
than  it  is  in  the  case  of  the  nearer  stars  which  have 
larger  values  of  r  $  the  diminution  in  the  number  of 
zero  motions  is  still  more  remarkable.  This  arises 
from  the  fact  that  in  the  case  of  the  nearer  stars  the 
apical  motions  are  necessarily  larger,  whether  positive 
or  negative. 

In  the  preceding  table  all  the  stars  were  counted, 
without  reference  to  their  distance  from  the  solar 
apex.  The  result  of  this  will  be  that  the  mean  of  the 
apical  motions  is  taken  as  we  see  it  projected  on  the 
sphere,  which  does  not  correspond  to  the  actual 
motion  in  space  except  when  the  direction  of  the  star 
is  at  right  angles  to  that  of  the  apex.  I  have,  there- 
fore, made  a  second  partial  count,  including  only  stars 
between  60°  and  120°  from  the  apex.  These  stars 
were  selected  in  opposite  regions  of  the  heavens,  so 
as  to  eliminate  any  constant  error  depending  on  the 
right  ascension.  The  result  of  a  count  of  733  stars  is  : 

Number  of  positive  motions   530 

"    zero  50 

"    negative  153 

If  we  proceed  as  before,  dividing  the  zero  motions 
equally  between  the  positive  and  negative  ones,  we 
shall  find  the  respective  numbers  to  be  555  and  178. 


AVERAGE  SPEED  OF  A  STAR  303 

The  percentage  of  negative  motions  is,  therefore,  24. 
This  will  still  be  slightly  too  large,  owing  to  the 
obliquity  under  which  many  of  the  stars  were  seen. 
We  may  estimate  the  most  likely  percentage  as  23. 

We  conclude  that  when  the  motions  of  all  the 
stars  are  so  resolved  that  one  component  shall  be 
that  in  the  direction  of  the  apex,  23  per  cent,  of  the 
stars  will  be  found  moving  towards  the  apex  with  a 
greater  speed  than  that  of  the  sun.  It  may,  there- 
fore, be  assumed  that  in  the  genera-1  average  an  equal 
number  are  moving  in  the  opposite  direction  with  a 
greater  speed  than  that  of  the  sun.  We  conclude 
that  the  resolved  motion  of  46  per  cent,  of  the  stars  is 
greater  than  that  of  the  sun,  leaving  54  per  cent.  less. 

In  the  absence  of  an  exact  knowledge  of  the  rela- 
tion between  the  magnitude  and  the  number  of 
motions,  we  shall  not  be  far  wrong  in  assuming  that 
one-half  the  stars  move  to  or  from  the  apex  with  more 
than  the  average  speed,  and  one-half  with  less.  Com- 
paring this  with  the  percentage  found,  we  may  con- 
clude that  the  average  motion  of  a  star  is  less  than 
that  of  the  sun,  in  the  ratio  46  :  50  ;  or  that  it  is  found 
by  multiplying  the  motion  of  the  sun  by  the  factor 
0.92.  This  is  almost  exactly  the  number  which  we 
have  quoted  from  Kapteyn. 

We  have  already  stated  that  the  actual  speed  of  the 
solar  motion,  still  somewhat  uncertain,  may  be  esti- 
mated at  20  kilometres  per  second,  or  4  radii  of  the 
earth's  orbit  in  a  year.  For  our  present  purposes  the 
latter  method  of  expressing  the  velocity  is  the  more 
convenient.  Multiplying  this  speed  by  the  factors 


304    STATISTICAL  STUDIES  OF  PROPER  MOTION 

already  found,  we  have  the  following  results  for  the 
average  proper  motions  of  a  star  in  space  expressed 
in  kilometres  per  second,  and  radii  of  the  earth's  orbit, 
called  R,  in  a  year : 

Straight-ahead    motion 35km.  =  7.4!*.. 

Projected  motion 28km.  =  5.8R. 

Motion  in   one  component....  i8km.  =  3-7R. 

The  motion  of  igkm.  or  4R.  assigned  to  the  sun  is 
its  straight-ahead  motion.  This  is  little  more  than 
half  the  average.  It  follows  that  our  sun  is  a  star  of 
quite  small  proper  motion. 


CHAPTER    XX 
THE  DISTRIBUTION  OF  THE  STARS  IN  SPACE 

Hoc  opus  immensi  constructum  corpore  mundi 
Membraque  naturae  di versa  condita  forma. 
^Eris  atque  ignis  terrae  pelagique  jacentis, 
Vis  anima  divina  regit — 

MANILIUS. 

WE  shall  now  bring  the  lines  of  thought  which  we 
have  set  forth  in  the  preceding  chapters  to  con- 
verge on  our  main  and  concluding  problem,  that  of 
the  distribution  of  the  stars  in  space.  While  we  can- 
not reach  a  conclusion  that  can  claim  numerical  exact- 
ness, we  may  reach  one  that  will  give  us  a  general 
idea  of  the  subject.  The  first  question  at  which  we 
aim  is  that  of  the  number  of  stars  within  some  limit 
of  distance.  It  is  as  if,  looking  around  upon  an  ex- 
tensive landscape  in  an  inhabited  country,  we  wished 
to  estimate  the  average  number  of  houses  in  a  square 
mile.  On  the  general  average,  what  is  the  radius  of 
the  sphere  occupied  by  a  single  star  ?  If  we  divide  thei 
number  of  cubic  miles  in  some  immense  region  of 
the  heavens  by  the  number  of  stars  within  that  region, 
what  quotient  should  we  get  ?  Of  course,  cubic  miles 
are  not  our  unit  of  measure  in  such  a  case.  It  will 
305 


306     DISTRIBUTION  OF  THE  STARS  IN  SPACE 

be  more  convenient  to  take  as  our  unit  of  volume  a 
sphere  of  such  radius  that,  from  its  centre,  supposed 
to  be  at  the  sun,  the  annual  parallax  of  a  star  on  the 
surface  would  be  i".  The  radius  of  this  sphere  would 
be  206,265  times  that  of  the  earth's  orbit.  We  may 
use  round  numbers,  consider  it  200,000  of  these  radii, 
and  designate  it  by  the  letter  R. 

Now  let  us  conceive  drawn  around  the  sun  as  a  centre 
concentric  spheres  of  which  the  radii  are  R,  2R,  3R, 
and  so  on.  At  the  surfaces  of  these  respective  spheres 
the  parallax  of  a  star  would  be  i",  half  of  a  second, 
one-third  of  a  second,  and  so  on.  The  volumes  of 
spheres  being  as  the  cubes  of  their  radii,  those  of  the 
successive  spheres  would  be  proportional  to  the  num- 
bers i,  8,  27,  64,  etc. 

If  the  stars  are  uniformly  scattered  through  space, 
the  numbers  having  parallaxes  between  the  corre- 
sponding limits  will  be  in  the  same  proportion. 

The  most  obvious  method  of  determining  the  num- 
ber of  stars  within  the  celestial  spaces  around  us  is  by 
measurement  of  their  parallaxes.  It  is  possible  to 
reach  a  definite  conclusion  in  this  way  only  in  the 
case  of  parallaxes  sufficiently  large  to  be  measured 
with  an  approach  to  accuracy..  In  the  case  of  a  small 
parallax  the  uncertainty  of  the  latter  may  be  equal  to 
its  whole  amount.  In  this  case  the  star  may  be  at 
any  distance  outside  the  sphere  given  by  its  measured 
parallax,  or  far  within  that  sphere,  so  that  no  conclu- 
sion can  be  drawn.  It  is,  on  the  whole,  useless  to 
consider  parallaxes  less  than  o".  10;  even  those  hav- 
ing this  value  are  quite  uncertain  in  most  of  the  cases. 


THICKNESS  OF  THE  STARS  IN'  SPACE      307 

The  data  at  command  for  our  purpose  are  the  known 
individual  parallaxes  and  the  statistical  summary 
given  by  Dr.  Chase  as  the  result  of  his  survey  and 
quoted  in  our  chapter  on  the  parallaxes  of  the  stars. 
This  survey  was  confined  to  stars  whose  parallax  was 
not  already  measured,  and  it  brought  out  no  parallax 
exceeding  o'^o.1 

The  most  careful  search  has  failed  to  reveal  any 
star  with  a  parallax  as  great  as  i",  and  it  is  not  likely 
that  any  such  exists.  It  is,  therefore,  highly  probable 
that  the  first  sphere  will  not  contain  a  single  star 
except  the  sun  in  its  centre. 

Within  the  third  sphere,  the  parallax  at  the  surface 
of  which  is  o".33,  we  may  place  the  following  four 
stars : 

n 
a  Centauri Par.=o.75 

LI.  21,185 "      °-4^ 

6 1  Cygni , 0.39 

Sirius 0.37 

There  are  two  other  cases  in  which  the  parallax  is 
doubtful,  though  the  measures  as  made  bring  the 
stars  within  the  sphere  3R.  They  are  : 

rf  Herculis Par. =0.40 

O.  A.   18,609 °-3S 

In  the  case  of  Eta  Herculis  the  proper  motion  is 
so  small  that  the  presumption  is  strongly  against  so 
large  a  parallax,  and  the  doubtful  parallax  of  the  last 

1  The  results  of  this  survey  were  communicated  to  the  Astronomical  and 
Astrophysical  Society  of  America  toward  the  end  of  June,  1900,  and  published 
in  Science  with  the  Proceedings  of  the  Society. 


3o8     DISTRIBUTION  OF  THE  STARS  IN  SPACE 

star  is  so  near  the  limit  that  it  may  be  left  out  of  the 
count.  The  doubt  in  its  case  may  be  set  off  against 
a  doubt  whether  the  parallax  assigned  to  LI.  21,185 
is  not  too  large.  We  assume,  therefore,  that  four 
stars  are  contained  within  the  sphere  3R,  the  volume 
of  which  is  33=27.  This  would  give,  in  whole  num- 
bers, one  star  to  7  unit  spheres  of  space. 

When  we  come  to  smaller  parallaxes  we  find  a 
great  deficiency  in  the  number  measured  in  the  South- 
ern Hemisphere.  The  policy  of  Gill,  under  whose 
direction  or  with  whose  support  all  the  good  meas- 
ures in  that  hemisphere  were  made,  was  to  make 
a  few  very  thorough  determinations  rather  than  a 
general  survey.  Between  the  limits  o".2o  and  o". 33 
are  found  : 

In  the  Southern  Hemisphere 4  meas.  (Gill) 

"        Northern  "  2      "       (Chase) 

12      "       (others) 

Total 18 

Of  the  northern  results  three  are  exactly  on  the 
limit,  o".2O,  and  several  others  are  doubtful,  and  prob- 
ably too  large.  The  most  likely  number  for  the 
Northern  Hemisphere  seems  to  be  12,  and  if  we  es- 
timate an  equal  number  for  the  Southern  Hemisphere 
we  shall  have  24  in  all.  Adding  the  four  stars  within 
the  sphere  3R,  we  shall  then  have  a  total  of  28  within 
the  sphere  5R,  of  which  the  volume  is  125.  This 
gives  between  4  and  5  space  units  to  a  star. 

Let  us  now  consider  the  space  between  the  spheres 
5R  and  loR,  including  all  stars  whose  parallax  lies 


THICKNESS  OF  THE  STARS  IN  SPACE       309 

between   the  limits  o".  10  and  o".2o.     Of   these   the 
numbers  are  : 

Southern  Hemisphere 6  (Gill) 

Northern  15  (Chase) 

15   (others) 

Reasoning  as  before,  we  may  assume  that  the 
number  of  stars  between  the  assigned  limits  is  60, 
making  a  total  of  88  within  the  sphere  loR.  The 
volume  of  space  enclosed  being  1000  units,  this  will 
give  one  star  to  12  units  of  space. 

How  far  can  we  rely  on  this  number  as  an  approxi- 
mation to  the  actual  number  of  stars  within  the  tenth 
sphere  ?  The  errors  in  the  estimate  are  of  two 
classes,  those  affecting  the  parallax  itself  and  those 
arising  from  a  failure  to  include  all  the  stars  within 
the  sphere.  The  very  best  determinations  are  liable 
to  errors  of  two  or  three  hundredths  of  a  second,  the 
inferior  ones  to  still  larger  errors.  Thus,  it  may 
happen  that  there  are  stars  with  a  real  parallax  larger 
than  the  limit,  of  which  the  measures  fall  below  it 
and  are  not  included,  and  others  smaller  than  the 
limit,  which,  through  the  errors  of  measurement,  are 
made  to  come  within  the  sphere.  As  we  have  seen 
in  the  chapter  on  the  parallaxes,  it  is  quite  possible  that 
there  may  be  a  number  of  stars  with  a  measurable 
parallax  whose  proximity  we  have  never  suspected  on 
account  of  the  smallness  of  the  proper  motion.  We 
can  only  say  that  the  nearer  a  star  is  to  us  the  more 
likely  its  proximity  is  to  be  detected,  so  that  we  are 
much  surer  of  the  completeness  of  our  list  of  large 


310     DISTRIBUTION  OF  THE  STARS  IN  SPACE 

parallaxes  than  of  small  ones.  Hence,  there  may 
well  be  a  number  of  undetermined  parallaxes  upon 
or  just  above  the  limit  o".  10. 

The  most  likely  conclusion  we  can  draw  from  this 
examination  seems  to  be  that  in  the  region  around 
us  there  is  one  star  to  every  8  units  of  space ;  or  that 
a  sphere  of  radius  2R,  equal  to  412,500  radii  of  the 
earth's  orbit,  corresponding  to  a  parallax  of  ©".50, 
contains  one  star.  This  is  a  distance  over  which 
light  would  pass  in  6£  years. 

We  next  see  how  far  a  similar  result  can  be  de- 
rived from  statistics  of  the  proper  motions.  It  seems 
quite  likely  that  nearly  all  proper  motions  exceeding 
i"  annually  have  been  detected.  The  number  known 
is  between  90  and  100,  but  it  cannot  be  more  exactly 
stated  because  there  is  some  doubt  in  the  case  of  a 
number  which  seem  to  be  just  about  on  the  limit. 
In  this  value,  i",  is  included  the  effect  of  the  parallac- 
tic  motion,  which,  on  the  general  average,  increases 
the  apparent  proper  motion  of  a  star.  To  study  this 
effect  let  us  call  the  list  of  90  or  more  stars  act- 
ually found  List  A.  Were  it  possible  to  observe  the 
proper  motions  of  the  stars  themselves  separate  from 
the  parallactic  motion,  we  should  find  that,  when  we 
enumerate  all  having  a  proper  motion  of  more  than 
i",  we  should  add  some  to  our  List  A  and  take  away 
others.  The  stars  we  should  add  would  be  those 
moving  in  the  same  direction  as  the  sun,  whose 
motions  appear  to  us  to  be  smaller  than  they  really 
are,  while  we  should  take  away  those  moving  in  the 
opposite  direction,  whose  motions  appear  to  us  larger 


THICKNESS  OF  THE  STARS  IN  SPACE      311 

than  they  really  are.  On  the  average,  we  should 
take  away  more  than  we  added,  thus  diminishing 
slightly  the  number  of  stars  whose  motion  exceeds 
i".  Making  every  allowance,  we  may  estimate  that 
probably  80  stars  have  an  actual  proper  motion  on 
the  celestial  sphere  of  i"  or  more.  We  have  found 
that  the  average  linear  proper  motion  of  a  star,  as 
projected  on  the  sphere,  is  about  6  radii  of  the 
earth's  orbit  annually.  A  star  having  this  motion 
would  have  to  be  placed  at  the  distance  6R  to  have, 
as  seen  by  us,  an  angular  motion  of  i".  The  par- 
allax corresponding  to  the  surface  of  this  sphere  is 
o".  167.  The  volume  of  the  sphere  is  216,  and  accord- 
ing to  our  estimate  from  the  parallaxes  it  would  con- 
tain only  27  stars.  Thus  the  proper  motions  seem  to 
give  a  greater  density  of  the  stars  than  do  the  meas- 
ured parallaxes  ;  that  is  to  say,  they  indicate  that  there 
are  still  a  large  number  of  measurable  parallaxes  unde- 
termined. But  the  fact  is  that  the  number  of  stars 
estimated  as  within  a  given  sphere  by  the  proper 
motions  will  be  in  excess,  owing  to  the  actual  divers- 
ity of  these  proper  motions,  which  may  range  from  o 
to  a  value  several  times  greater  than  the  average. 
In  consequence  of  this,  our  list  of  stars  with  a  proper 
motion  exceeding  i"  will  contain  a  number  lying  out- 
side the  sphere  6R,  but  having  a  proper  motion 
larger  than  the  average.  We  are  also  to  consider 
that  within  the  sphere  may  actually  lie  stars  having 
a  proper  motion  less  than  the  average,  which  will, 
therefore,  be  omitted  from  the  list.  Of  the  number 
of  omitted  and  added  stars  the  latter  will  be  the 


3i2     DISTRIBUTION  OF  THE  STARS  IN  SPACE 

greater,  because  the  volumes  of  spheres  increase  as 
the  cubes  of  their  radii.  For  example,  the  space 
between  the  spheres  6R  and  9R  is  more  than  double 
that  within  6R,  and  our  list  will  include  many  stars 
in  this  space.  Thus  arises  a  discrepancy  between 
the  parallaxes  and  the  proper  motions.1 

Let  us  see  what  the  result  is  when  we  take  stars  of 
smaller  proper' motion.  The  most  definite  limit  which 
we  can  set  is  10"  per  century.  We  have  seen  that  Dr. 
Auwers,  in  his  zone,  found  23.9  stars  per  100  square 
degrees  having  a  proper  motion  of  10"  or  more.  This 
ratio  would  give  about  10,000  for  the  whole  heavens. 
The  sphere  corresponding  to  this  limit  of  proper 
motion  is  6oR.  On  our  hypothesis  as  to  star-density 
this  sphere  would  contain  27,000  stars,  nearly  three 
times  the  number  derived  from  Auwers's  work.  But 
it  is  not  at  all  unlikely  that  this  sphere  contains  three 
times  as  many  proper-motion  stars  as  have  been  de- 
tected. Great  numbers  of  the  more  distant  stars  will 
not  have  been  catalogued,  owing  to  their  faintness, 
because  a  star  at  the  distance  6oR  will  shine  to  us 
with  only  one  per  cent,  the  light  of  one  at  distance 
6R.  This  corresponds  to  a  diminution  of  five  magni- 
tudes ;  that  is  to  say,  a  star  of  the  sixth  magnitude 

1  The  principle  involved  in  the  case  may  be  more  fully  stated  thus  :  If  we 
take  all  the  stars  that  lie  within  a  given  sphere,  and  determine  their  proper 
motions  and  parallaxes,  we  shall  get  the  correct  relation  between  the  proper 
motions  and  parallaxes.  But  if  we  take  all  stars  whose  proper  motion  exceeds- 
a  certain  limit,  and  determine  their  parallaxes,  the  mean  of  these  parallaxes 
will  be  disproportionately  small,  owing  to  the  omission  of  stars  with  proper 
motions  below  the  limit,  but  lying  within  the  sphere  of  measurement.  It  thus 
happens  that  the  proper  motions  found  in  our  Appendix  II.  are,  in  the  general 
average,  much  more  than  six  times  the  parallax. 


THICKNESS  OF  THE  STARS  IN  SPACE      313 

at  distance  6R  would  only  be  of  the  eleventh  mag- 
nitude at  distance  6oR,  and  would,  therefore,  not  be 
catalogued  at  all.  There  is,  therefore,  no  reason  for 
changing  our  estimate  of  star-density,  which  assigns  to 
each  star  around  us  8  units  of  volume  in  space. 

This  fact  suggests  another  important  one.  Owing 
to  the  great  diversity  in  the  absolute  magnitude  of 
the  stars,  those  we  can  observe  with  our  telescopes 
will  naturally  be  more  crowded  in  the  neighbourhood 
of  our  system  than  they  will  at  greater  distances. 

Some  further  results  as  to  the  mean  parallax  of  the 
stars  may  be  derived  from  a  continuation  of  the  statis- 
tical study  of  the  proper  motions.  Kapteyn's  inves- 
tigation in  this  direction  includes  a  determination  of 
the  mean  parallactic  motion  of  the  stars  of  each  mag- 
nitude for  the  first  and  second  spectral  types  separately. 
From  this  he  obtains  the  following  mean  parallaxes 
for  stars  of  the  different  magnitudes  : 

Mean  parallaxes  of  stars  of  different  magni- 
tudes, and  of  the  two  principal  types,  as  found  from 
their  parallactic  motions  : 

Mag.  Type  I.  Type  II. 

I  IT 

2.0  .0315  .0715 

3.0  .0223  .0515 

4.0  .0157  .0357 

5.0  .our  .0253        .   ^ 

6.0  .0079  -0179 

7.0  .0056  .0126 

8.0  .0039  .0089 

9.0  .0028  .0063 

10.0  .0020  -0045 

n.o        .0014        .0032 


3i4     DISTRIBUTION  OF  THE  STARS  IN  SPACE 

Using  the  value  4  for  the  solar  motion,  instead  of  3.5,  found  by  Kapteyn.  all 
these  parallaxes  should  be  diminished  by  one  eighth  of  their  amount. 

Unfortunately,  owing  to  the  great  diversity  in  the 
absolute  brightness  of  the  stars,  and  the  resulting 
great  difference  in  the  distances  of  stars  having  the 
same  magnitude,  these  numbers  can  give  us  no  idea 
of  the  actual  parallaxes.  Let  us  take,  for  example, 
the  stars  of  the  sixth  magnitude.  A  few  of  these 
ar^  doubtless  quite  near  to  us  and  have  a  parallax 
several  times  greater  than  that  of  the  table.  Exclud- 
ing these  from  the  mean,  an  important  fraction  of  the 
remainder,  perhaps  a  great  majority,  may  have  a 
parallax  smaller  than  that  of  the  table  to  any  extent 
—  may,  in  fact,  be  on  the  very  confines  of  the 
universe.1 

We  get  a  slightly  more  definite  result  by  studying 
another  feature  of  the  proper  motions.  We  may  con- 
sider the  Bradley  stars,  whose  motions  have  been  in- 
vestigated, as  typical  in  the  general  average  of  stars 
of  the  sixth  magnitude.  By  a  process  of  reasoning 
from  the  statistics,  of  which  I  need  not  go  into  the 
details  at  present,  it  is  shown  that  the  parallactic  mo- 
tion of  a  large  number  of  these  stars,  probably  one- 
sixth  of  the  whole,  is  less  than  \"  per  century.  To 

1  Since  the  present  work  was  prepared  for  the  press,  Kapteyn  has  published 
a  number  of  careful  and  intricate  researches  on  stellar  statistics,  bearing  on  the 
subject  discussed  in  this  and  the  next  chapter.  One  of  these  papers,  forming 
No.  8  of  the  Publications  of  the  Astronomical  Laboratory  at  Groningtn,  is  "on 
the  mean  parallax  of  stars  of  determined  proper  motion  and  magnitude "  ; 
another,  published  in  the  Proceedings  of  the  Amsterdam  Academy  for  April 
20,  ryoi,  is  "on  the  luminosity  of  the  fixed  stars."  So  far  as  the  results 
worked  out  in  these  papers  bear  on  the  problem  of  the  extent  of  the  universe, 
the  reasoning  is  too  abstruse  and  the  results  too  mathematical  to  be  easily 
presented  in  the  present  work. 


THICKNESS  OF  THE  STARS  IN  SPACE      3.5 

this  motion  corresponds  a  parallax  of  o".oo25,  corres- 
ponding to  the  sphere  of  radius  4OoR. 

The  statistics  of  cross  motions  lead  to  a  similar  con- 
clusion. One-half  the  Bradley  stars  have  a  cross 
motion  of  less  than  2".$  per  century.  To  this  motion 
would  correspond  a  sphere  of  radius  2OoR  and  a 
parallax  of  o".oo5.  Stars  at  this  distance  must  be 
hundreds  of  times  the  absolute  brightness  of  the  sun 
to  be  seen  as  of  the  sixth  magnitude.  Yet  the  con- 
clusion seems  unavoidable  that  the  sphere  of  lucid 
stars  extends  much  beyond  4OoR. 

We  shall  next  make  an  estimate  based  on  the  num- 
ber of  the  stars.  All  the  facts  we  have  reviewed  leacl 
to  the  belief  that,  out  to  a  great  distance,  the  stars 
are  scattered  without  any  great  and  well  marked 
deviation  from  uniformity.  This  belief  rests  upon 
the  remarkable  equality  in  the  number  of  stars  in 
opposite  directions  from.  us.  We  do  not  detect  any 
marked  difference  between  the  numbers  lying  round 
the  two  opposite  poles  of  the  galaxy,  nor,  so  far  as 
known,  between  the  star  density  in  different  regions 
at  equal  distances  from  the  Milky  Way.  Accepting 
this  view,  the  question  how  far  we  must  place  the 
boundary  of  a  sphere  in  order  that  it  may  contain  a 
given  number  of  stars  admits  of  a  definite  answer. 
We  have  only  to  extract  the  cube  root  of  the  num- 
ber, and  multiply  it  by  2.  Consequently  the  sphere  of1 
radius  2«R  will  contain  n3  stars.  Thus  a  sphere  of 

Radius  4ocR  will  contain  8,000,000  stars 
"      6ooR    "         "       27,000,000      " 


3i6     DISTRIBUTION  OF  THE  STARS  IN  SPACE 

Radius  8ooR  will  contain  64,000,000  stars 
'     loooR    '  125,000,000 

The  minutest  counts  of  stars  that  have  been  made, 
and  the  photometric  law  shown  in  the  beginning  of 
Chapter  XVIII.  lead  us  to  suppose  that  the  actual 
number  of  non-galactic  stars,  visible  and  invisible, 
probably  falls  within  the  limits  of  the  above  numbers. 
We  have  therefore  no  reason  to  believe  that,  away 
from  the  Milky  Way,  the  stars  extend  far  beyond 
the  sphere  loooR,  at  whose  boundary  the  parallax  is 
o".ooi,  and  the  average  proper  motion  of  a  star  about 
o".6  per  century.  But  the  phenomena  of  the  Milky 
Way  show  that  around  the  region  of  the  galactic  belt, 
there  is  a  distance  at  which  the  law  of  uniform  density 

ceases  to  be  true.  Let 
S  be  the  sun,  Ri  a 
portion  of  the  surface 
of  the  outer  sphere  of 
uniform  distribution, 
and  R2  and  R3  two 
contiguous  spheres 
passing  through  the 
galactic  region  G,  of 
which  the  pole  is  in 
the  direction  P.  It 
is  quite  certain  that 
the  star -density  is 
greater  around  G  than  around  P.  This  may  arise 
either  from  the  density  at  G  being  greater,  or  from 
that  at  P  being  less  than  the  density  within  the 
sphere  Ri.  From  the  enormous  number  of  stars 


DISTANCE  OF  STARS  IN  THE  MILKY  WAY  317 

collected  in  the  galactic  regions,  we  can  scarcely  doubt 
that  the  former  alternative  is  the  correct  one.  But 
there  must  be  a  sphere  at  which  the  second  alternative 
is  also  correct,  because  we  find  the  number  of  stars, 
even  of  the  lucid  ones,  to  continuously  increase  from 
P  toward  G. 

Can  we  form  any  idea  where  this  difference  begins, 
or  what  is  the  nearest  sphere  which  will  contain  an 
important  number  of  galactic  stars  ?  A  precise  idea, 
no ;  a  vague  one,  yes.  We  have  seen  that  the 
galactic  agglomerations  contain  quite  a  number  of 
lucid  stars,  and  that,  perhaps,  an  eighth  of  these  stars 
are  outside  the  sphere  4OoR.  We  may,  therefore, 
infer  that  the  Milky  Way  stars  lie  outside  this 
sphere.  Considerations  based  on  the  proper  motions 
lead  us  to  place  these  stars  even  outside  the  sphere 
lOOoR.  It  seems  certain  that  the  blue  stars  of  the 
constellation  Orion  have  a  proper  motion  of  only  a 
small  fraction  of  a  second  per  century — a  few  tenths 
or  less.  Although  these  do  not  belong  to  the  Milky 
Way  itself,  there  is  reason  to  believe  that  they  do 
not  lie  beyond  it,  and  that  the  proper  motions  of  the 
stars  of  the  Milky  Way  are  equally  small.  This 
would  place  the  stars  of  the  Milky  Wray  at  a  greater 
distance  than  the  probable  confines  of  the  universe  in 
the  direction  of  the  galactic  poles. 

So  far  as  we  can  judge  from  the  enumeration  of 
the  stars  in  all  directions,  and  from  the  aspect  of  the 
Milky  Way,  our  system  is  near  the  centre  of  the  stel- 
lar universe.  That  we  are  in  the  galactic  plane  itself 
seems  to  be  shown  in  two  ways  :  (i)  the  equality  in 


3i8    DISTRIBUTION  OF  THE  STARS  IN  SPACE 

the  counts  of  stars  on  the  two  sides  of  this  plane  all 
the  way  to  its  poles,  and  (2)  the  fact  that  the  central 
line  of  the  galaxy  is  a  great  circle,  which  it  would 
not  be  if  we  viewed  it  from  one  side  of  its  central 
plane. 

Our  situation  in  the  centre  of  the  galactic  circle,  if 
circle  it  be,  is  less  easily  established,  because  of  the 
irregularities  of  the  Milky  Way.  The  openings  we 
have  described  in  its  structure,  and  the  smaller  dens- 
ity of  the  stars  in  the  region  of  the  constellation 
Aquila,  may  well  lead  us  to  suppose  that  we  are  per- 
haps markedly  nearer  to  this  region  of  its  centre  than 
to  the  opposite  region  ;  but  this  needs  to  be  estab- 
lished by  further  evidence.  Not  until  the  charts  of 
the  International  Photographic  Survey  of  the  heavens 
are  carefully  studied  does  it  seem  possible  to  reach  a 
more  definite  conclusion  than  this. 

One  reflection  may  occur  to  the  thinking  reader,  as 
he  sees  these  reasons  for  deeming  our  position  in  the 
universe  to  be  a  central  one.  Ptolemy  showed  by 
evidence  which,  from  his  standpoint,  looked  as  sound 
as  that  which  we  have  cited  that  the  earth  was  fixed 
in  the  centre  of  the  universe.  May  we  not  be  the 
victims  of  some  fallacy,  as  he  was  ? 

The  following  is  a  summary  of  more  or  less  prob- 
able conclusions,  drawn  from  facts  developed  in  the 
present  work  : 

i.  The  stars  differ  enormously  in  their  actual  lumin- 
osity. Some  are  thousands  or  tens  of  thousands  of 
times  more  luminous  than  the  sun  ;  others  only  one- 
hundredth  or  one-thousandth  as  luminous. 


SUMMARY  OF  CONCLUSIONS  319 

2.  The  more  luminous  stars  are  generally  the  hot- 
ter,  the    bluer,   and  the   rarer  in   their  constitution. 
They  are,  as  it  were,  inflated  masses  of  rare  and  in- 
tensely incandescent  gas.      Hence  the  stars  do  not 
differ  in  mass  so  widely  as  in  luminosity. 

3.  The  bluest  and  most  luminous  stars  are  situate 
mainly  in  the  region  of  the  Milky  Way.     There  is 
some  reason  to  suspect  that  in  this  region  the  more 
densely  the   stars  are   agglomerated  the  larger  and 
more  luminous  they  are. 

4.  That  collection  of  stars  which  we  call  the  uni- 
verse is  limited  in  extent.     The  smallest  stars  that 
we  see  with  the  most  powerful  telescopes  are  not,  for 
the    most   part,    more    distant    than    those    a    grade 
brighter,    but    are    mostly    stars   of   less    luminosity, 
situate  in  the  same  regions.      This  does  not  preclude 
the  possibility  that  far  outside  of  our  universe  there 
may  be  other  collections  of  stars  of  which  we  know 
nothing. 

5.  The  boundary  of  our  universe  is  probably  some 
what  indefinite  and  irregular.     As  we  approach  it,  the 
stars  may  thin  out  gradually.     The  parallax  at  the 
boundary  is  probably  nowhere  greater   than  o".ooi, 
and  may  be  much  less.     The  time  required  for  light 
to  pass  over  the  corresponding  interval  is  more  than 
three  thousand  years. 

6.  The  universe  extends  farther  around  the  girdle 
of  the   Milky  Way   than   toward   the  poles  of  that 
girdle.      But,   in  every  direction,   it  extends  beyond 
the  limit  within  which  the  proper  motions  of  the  stars 
have  yet  been  determined. 


320  SUMMARY  OF  CONCLUSIONS 

7.  It  does  not  yet  seem  possible  to  decide  whether 
the   agglomerations   of   the   Milky   Way  lie   on   the 
boundary   of  the   universe  or  not.     The  number  of 
lucid  stars  which  they  contain  might  seem  to  militate 
against  the  view,  though  not  strongly  because  of  the 
possible  great  luminosity  of  the  galactic  stars. 

8.  The  total  number  of  the  stars  is  to  be  counted 
by  hundreds  of  millions. 

9.  Outside  the  galactic  region  the  stars  in  general 
show  no  tendency  to  collect  into  systems  or  clusters, 
but  are  mostly  scattered   through  space  with  some 
approach  to  uniformity. 


APPENDIX 

In  this  appendix  are  found  lists  of  the  individual  names  of 
certain  stars,  of  parallaxes  and  large  proper  motions,  and  of  spec- 
troscopic  binary  systems. 

The  list  of  names  seems  to  require  no  explanation. 

List  of  parallaxes  and  proper  motions. 

The  parallaxes  in  this  list  are  derived,  for  the  most  part,  from 
a  combination  of  all  the  investigations  or  authorities  on  the 
subject. 

A  colon  after  a  parallax  indicates  that  it  is  subject  to  more 
doubt  than  usual ;  two  colons,  that  it  is  entirely  unreliable. 

The  numbers  and  letters  in  the  column  "  light "  are  intended 
to  show  the  luminosity  of  the  star,  or  the  ratio  of  the  actual 
amount  of  light  emitted  from  its  entire  surface  Lo  that  emitted 
from  the  entire  surface  of  the  sun.  The  numbers  cannot  lay  any 
claim  to  exactness,  owing  to  the  uncertainty  as  to  the  star's  exact 
distance  from  us,  and  are  intended  only  to  give  a  general  idea  of 
the  actual  magnitude  or  luminosity  of  the  star. 

Where  the  letters  XM  are  used  in  this  column  they  mean  that 
no  numerical  statement  is  possible  except  that  the  star  is  thou- 
sands and  perhaps  tens  or  even  hundreds  of  thousands  of  times 
brighter  than  the  sun. 

List  of  spectroscopic  binary  systems  established  to  July,  IQOI. 

This  is  a  list  of  stars  for  which  a  variability  of  the  radial  motion 
supposed  to  be  due  to  the  action  of  a  companion  or  the  duplicity 
of  the  star  has  been  established. 

The  period  is  given  in  days. 

The  orbital  velocity  is  the  extreme  deviation  of  the  observed 
orbital  velocity  from  the  mean,  smoothed  off  where  the  observa- 
tions are  sufficiently  numerous.  In  those  cases  where  an  orbit 
321 


322 


NAMES  OF  STARS 


has  been  computed  from  the  observed  velocities,  the  velocity 
given  is  that  derived  from  the  elements. 

It  will  be  noted  that  in  many  cases  the  period  and  velocity  are 
not  yet  determined. 

The  author  is  indebted  to  Professor  Campbell  for  most  of  the 
particulars  given  in  the  list,  and  for  its  final  revision. 

I.  Names  of  individual  stars  found  in  astronomical  literature^  with 
their  approximate  positions  for  1900. 


Individual  Name. 

Name  on  Bayer  System. 

Position  for  1900. 

R.  A. 

Dec. 

h        m 
I     34.0 

13      21.2 

3    41-5 
4     30.2 
o      8.1 

3       1-7 
12    49  8 

19    45-9 
16    23.3 
14     ii.  i 
5     198 
5     49-8 
6     21.7 
5       9-3 
o      3.8 

7     28.2 
'4     51-3 

20      38.0 

ii     44-0 
10    57.6 

22      52  I 

22     59-8 

2      14-3 
13      19-9 
I       22.5 

7     39-2 
7     34-1 
10      3.0 
5      9-7 
6    40.7 

13     19-9 
18     33.6 

-57     55 
+55     30- 
+23     48 
+  16     18 
+  14     38 
+40    34 
+56     29 
+  8     36- 
-26     13 
+19    42 
+  6     16 
+  7     23 
-52     38 
+45     54 
+58     36 
+32      6 
+38     52 
+44     55 
+  15       8- 
+62     17 
-30       9 
+  14     40 
-   3     26 
+55     27 
+88    46 
+28     16 
+  5     29. 

+  12      27 

-  8     19 
-16     35 
—  10    38 
+38     41 

Alcor 

80  Ursae  Majoris  
7?  Tauri  

Alcyone  

Algenib  

Algol 

Y  Pegasi  ... 

Alioth 

Altai  r 

<x  Bootis 

Y  Orionis 

Betelguese       

oc  Orionis  

Canopus  

ex.  Argus  (Carinae)  

Capella  

a  Aurigae  

Caph 

Castor 

Cor  Caroli  

a  Canum  Venaticorum.   .... 

"fygni  

Deneb  

Denebola 

Dubhe 

oc.  Piscis  Australis  

Markab  
MiraCeti  
Mizar 

a  Pegasi  
oCeti  

Polaris  

a  Ursae  Minoris  

Pollux 

Procyon  
Regulus  

a  Canis  Minoris  
a  1  .eonis  
ft  Orionis  
<x  Canis  Majoris  

Spica 

Vega  

a  Lyrae  

PARALLAXES  AND  PROPER  MOTIONS       323 


//.  List  of  parallaxes  of  stars  and  of  proper  motions  exceeding 
100"  per  century. 


Star. 

Position,  1900. 

Par- 
allax. 

•a? 

Lumi- 
nosity. 
0=i. 

Annual  Proper 
Motion. 

R.  A. 

Dec. 

R.  A. 

Dec. 

B  Cassiopeiae. 

h     m 
o     3.8 
o  12.7 

0   14-9 

o  20.5 
o  32.2 
o  34.8 
o  43  o 
o  43-1 
o  50.7 
I     1.6 

I   22.6 
I   34.0 

i  39-4 
2     6.4 

2    II.O 
2    3O.6 
2    56.0 

3     1.8 
3  15-6 
3  15-9 
3  16.0 
3  28.2 
3  40.2 
3  56.5 
4     i-9 
4  IO-7 
4  30.2 
4  55-8 
5     7-7 
5     7-7 
5     9-7 
S  26.4 
5  45-1 
5  49-8 
5  52.2 
6  21.7 
6  39-5 
6  40.7 
6  53-7 
7  28.2 
7  34-0 

+58  36 
+43  27 
-65  28 
-77  49 
-25  19 
+55  59 
+57  17 
+  4  46 
+60  10 
+54  26 
+88  46 
-57  45 
-16  28 
51  19 

0.15 
0.30: 
O.O6 
0.13 

0.04: 
0.20 

O.OI. 
0.14 
O.06 
O.O4 
0.31 

0.14 
0.04:: 

0.18 

O.II 

0.09 
o.oo 

0.02 
O.O6: 
O.OO 
O.II 

0.37 

0.03: 
0.20: 
0.30 

M 

2.4 

8.1 

4.3 
2.9 

5-6 

2.4 
3-6 

5-7 
2-3 

5-2 
2.1 

o.5 
3-7 
6.4 
5-0 
5-9 
6-7 
4.2 

6.2 

4-3 

5-8 
3-8 

8.2 

8.5 
5-5 
4-5 
i.i 
6.4 
8.5 

O.2 
0-3 

8.7 
6.5 
0.9 

2.1 
—  I.O 
5-3 
—  1.4 
5-2 

1.6 
0.5 

5 

O.OI 

6 

5 

50 

i 

IOOO 

0.5 
50 

0.5 

I 

5 
57 
45 

1  20 
XM 

500 
48 
XM 
0.7 
30 
ii 
7 
8 

+0.068 
+O.262 
+0.273 
+0.703 
+O.  IOO 

+0.006 
+0.143 
+0.048 
+0.004 
+0.391 
+0.136 

+O.OIC 
—O.I  2O 

+0.225 
+0.091 

+O.I2O 
+0.094 
+0.133 
+0.195 
+0.28I 

+0.192 
-0.066 
+0.053 
+0.143 
+0.014 

o  148 

—o.i  8 
+039 
-4-1.16 

+0.32 
o.oo 
—  o  03 

-048 

-1.13 

o.oo 

-1-55 
o.oo 
—0.04 
+0.86 
+0.72 
-0.23 

+  1.46 
-0.68 

—  O.IO 

+0.65 
+0.76 

+0.66 

+0.02 
—  0.12 
-1-34 
—  0.18 

-344 
-0.19 
i  n 

Gr   34       

C  Tucani   

ft  Hydri    

82  B  Ceti  

147  B  Piscium 

Polaris  

a  Eridani  

r  Ceti 

Lac   66  1 

+33  46 
H-  6  25 
+6  1  20 

+49  J4 
-62  58 
-43  27 
-62  53 
—  9  48 
+4i     9 
+35     2 
+37  47 
+  17  48 
6  18 

128  H  >  Ceti  

Lac  5490  

i  Persei   

£  '  Reticuli  

e  Eridani  

Ca  Reticuli             . 

LI   6888  

LI   7443    

50  Persei      

o*  Eridani 

+0.005 
4-0.040 
+0.621 

+0.009 

o.ooo 
+0.046 

+0.087 

+0.002 
—  0.004 
+O.O02 
+0.002 
-0.037 
+0.057 
—O.OI4 
—0.047 

Weisse   1189 

-  5  52 
-45     3 
+45  54 
-  8  19 
-  3  42 
-80  33 
+  7  23 
+44  56 
-52  38 
+43  4i 
-'6  35 
+87  12 
+32     6 
+  5  29 

C   Z  Vh    243 

-5-70 
—043 
o.oo 

—  2.12 
+  1.09 
+O.OI 
—  O  01 
+O.OI 

+o  16 

—  1.  21 
—O.O4 
—0.08 
-1.04 

Capella 

Rigel           

Weisse    592  

n  Mensse  

$  5  Aurigse  

Sirius  ,  

51  H   Cephei 

Castor 

324 


PARALLAXES  AND  PROPER  MOTIONS 


Star. 

Position,    1900. 

Par- 
allax. 

Magni- 
tude. 

Lumi- 
nosity 
0=i. 

Annual  Proper 
Motion. 

R.A. 

Dec. 

R.A. 

Dec. 

Pollux              .... 

h     m 
7  39-2 
7  41-8 
7  47-2 
7  54-3 
8  13.6 

8  29.0 
8  46.0 
8  52.4 
8  54.2 
976 
9  26.2 
9  37i 
9  46.2 
9  55-2 
10     3.0 
10    5.2 
10  21.9 
10  27.7 
10  57-9 
II     0.5 
ii     8.6 
II  148 
ii  29.6 

"  33-5 
ii  40.3 

ii  41.8 
ii  47.2 
"  53-0 

12      4.6 
12    IO.O 

13     7.2 

13    13-2 
13  40.2 
13  40-7 
13    56.8 
14    II.  I 
14   32.8 

14  4&.( 
14  51-6 
14  52.4 
15     4-7 
15     4-7 
15     8.8 
15  37-7 
15  51-8 

+28  16 
-33  59 
+30  55 
+29  3i 
—  12  18 

-31   ii 

+71   ii 
+48  26 
+42  ii 
+53     7 
+52     8 
+43  10 
—  ii  49 
+32  25 
+  12   27 
+49  58 
+49  lf) 
+49  42 
+36  38 
+44     2 

+74     I 

+66  23 
02    l8 

O.06 
0.02 

0.13: 
0.2O 
0.15 
O.O7 
O.O6 

O.O6 
0.02 

0.18 

0.10 

0.04 
0.46 

0.22 
0.15 
O.27: 
O.O3 
0.02 

O.O6 
0.14 
O.II 

0.05 
0.03 
0.75 

0.08 

M 
1.2 

5-4 

8.2 

7-0 
6.0 

6.4 
8-5 
3-i 
4.2 
8.0 

3-3 
8.0 
9-3 
5-5 
i-3 
6.8 
6.5 
7.6 
7.6 
8.5 

7-2 

9.0 
6.0 
6-3 
7.8 
5.o 
6.4 

7-2 

7-4 
6.0 

4-3 
4.8 
9.2 
8-5 
0.8 

0.3 

0.2 

7-8 
5-8 
7-7 
9-3 

9-2 

6.7 
7-3 
4.0 

100 

1.6 

3 
0.6 
0.03 

1  10 
O.2 

2 

IOOO 

0.07 
0.3 
0.7 
0.005 

O.OI 

0.07 
0.004 

4 

2 
0.2 

0.4 
1.9 

220 
IOOO 
1-7 

O.I 

s. 

-0.047 

—  O.O2I 
+0058 
—  0.012 
+0.017 
-0.088 
—0.280 
—0.044 
—0.039 
-0.175 
—O.IO3 
+O.O02 
+0.085 
—O.042 
—O.OI? 
—0.140 
+0.01  1 

+0.024 
-0.044 

—0.402 
—0.105 

-0.503 
-0.053 
—0.060 
—  0.061 

-0.133 
+0.341 
—0.074 
—0.029 
+0.005 
—0.060 
-0.075 
+0.027 
+0.125 
—o  003 
—0.078 
-0485 
—0.066 
+0074 

—  0.1IO 

—0.067 
—0.066 
—  o.oSs. 
—0.076 

+O.O2I 

—  0.06 
+  1.67 
-1.82 
-1.  17 
-0.99 

+0.69 

-0.35 
—0.25 
—0.26 
—0.62 

-0.54 
-0.80 
-1.50 
-0.44 
o.oo 

-0.52 

o  80 

Lac   20^7 

1.1.   15290  
LI     15565  

LI    16304  

1  ac   T?86 

Fed    1384 

e  Ursse  Maj 

Fed   1457-8 

6  Ursas  Maj  

LI.  19022    

Weisse    954  

20  Leo  Min  

Regulus  

Gr    1618   

Gr    1646     

Gr    1657   

+0.1  1 

-474 
+0-95 

+0-13 
+0.24 
+0.84 
+0.03 
o  28 

Ll    21185   

I.I.  21258  

Fed    1831 

O   A   11677 

Brad    1584 

2  H6I  

+45  40 
+48  14 

-39  57 
+38  26 
—27     8 
+40  49 
-  9  44 
+28  23 
-17  45 
+  18  20 
+  15  26 
-59  53 
+  19  42 
60  25 

Gr    1822  ...      . 

Lac.  4887  

+0.39 
-5-78 
-0.70 
—  o  06 

—  I.OI 

+0.88 
-1.07 

-1.85 

-1-47 
—0.03 

—  2.CO 

+0.73 
—  0.48 

-1.79 

+0.48 

-3.64 
-3.63 
-°-93 
-0-34 
-1.29 

Gr.  1830  

Lac.  4955  

Gr.  1855  

Ll.  22954  

Auwers  A.  G.  4999  
Aron  

ft  Centauri  

Ll    27026             

-23  53 

—  20    58 

454     4 
-15  59 
-15  54 
—  o  58 
—  in  36 
+  15  59 

43  B  Librae     

Fed.  2544  

O  A    14318 

O   A    14320 

Ll    27744      

Ll   28607  

Y  Serpentis  

PARALLAXES  AND  PROPER  MOTIONS       325 


Star. 

Position,    1900. 

Par- 

allax. 

•as- 

Lumi- 
nosity 

0=x. 

Annual  Proper 
Motion. 

R.  A. 

Dec. 

R.  A. 

Dec. 

Antares  
LI.  30044  

k      m 
16  23.3 
16  25.6 
16  39-5 
16  47.9 
16  50.1 
16  59.8 
17    9.2 
17  10.  i 
17  10.9 
17  II.  6 

17    12.2 
17    16.9 

17  20.8 
17  30.2 

17  37-0 
18    0.4 
18     4.5 
18  33.6 
18  41.7 
18  53-1 

19   20.  2 
19   32.6 
19  45-9 
19  55-6 
19  58.9 

19  59-7 
20    4.6 
20    9.0 

20   17.7 
20   38.0 
20   51.0 
21      2.4 
21    II.  4 
21    l6.2 
21    24.5 

21  55-7 

22      1.9 
22    16.0 
22    52.1 

22  59-4 
23     8.5 

23    II.Q 

23  44-o 
23  57-0 
23  5Q  5 

—  26   13 

+  4  26 
+39     7 

+   O    II 

-  8     9 

O.O2 
O.4O: 

o.ii: 
0.05: 

0.32 

O.22 
O.lg 
0.03: 
O.II 
0.35: 

O.O6 
O.26: 
O.23 

o.oo 

0.39 
0.06: 

0.2O 
0.02 

0.13 
0.28 

0.15 
0.05 

M 

5:3 

3-7 

6.8 
8.8 

7-9 
4.6 

6.7 
3-3 
5-9 

3-2 

5-4 
8.0 
4-9 
7-9 
4.1 
4-4 

O.I 

8.9 
9-3 

5-3 
4.8 
0.9 
6.6 
3.6 

7-2 

5-4 
5-8 

8.2 

1-3 

7-5 
4.8 
6.8 
2.6 

9.1 
4.8 
1.9 
5-8 
i.3 
7-4 
5-6 

8.2 

8.7 
5.8 
8.5 

900 
0.3 

4.7 
25 

O.I 
0.02 

0.7 

22 
90 
O.OO7 

2.5 
O.2 
10 

XM 

O.I 

30 

0.4 
500 

21 
O.O2 

o.3 

2.2 

s. 

—  0.001 

—0.030 
+0.003 
-0.049 
—0.063 
—0.062 

-0.037 

o  038 

—0.03 

—0-39 
—0.09 
-1.49 
—0.87 

-1-15 
—  1.17 

T>  Herculis  

LI    30694 

Weisse    906 

LI.  31055 

A.  Ophiuchi  
Brad.  2179       

-26  27 
—  26  24 
H-36  55 
+34  53 
+24  57 
+32  36 

+   2    14 

+  55  15 
-j-68  26 

+  2  31 
+86  37 
+38  41 
+59  29 
+  5  48 
+11  44 
+  69  29 
+  8  36 
67   "34 

—  O.OOI 

+0.096 

+O.002 

+0.009 

—0.040 
+0.018 

+0.069 

o  018 

o.oo 

—  0.21 

—o.i  6 

-1.05 

—  1.22 
+0.05 
—  1.25 
I  12 

Lac.  7215  

8  Herculis 

Weisse    322 

O.  A    17415     .  .  . 

70  Ophiuchi  

d  Ursae  Min  

+0.019 
+0.018 
—0.171 
—  0.016 
+0.050 

+O.IOO 

+0.036 

+0.186 
+0.192 
-0.074 
+0.037 
+0.094 
+0.037 

o.ooo 

+0.05 
+0.28 
+  1.87 
—  1.22 
+0.63 
-I.76 
+0.38 
—O.67 
—  I.I3 

-0.94 
-1.64 
-0.24 

—  I.IO 

o.oo 

-0.99 

+3.24 

—  1.22 
+0.05 
—0.28 
-2.58 
-o.iS 
-0.74 
-0.17 
+I-I5 
+0.30 
—  1.  21 
—  I.OO 
-0-99 
-2.58 

a  Lyrae  

Anon  

cc  Aquilse     

Lac.  8267  

LI.  38383  

+23     5 

—  36    21 
—  27    2O 
—  21    4O 

+44  55 

Lac.  8362  

Lac.  8381  

O   A   20452 

Lac.  8620  

+38  15 
-39  15 

+62    IO 
—  12    56 

+0.350 

—0.280 

+O.O22 

+0.070 

+0.479 

+0.01  1 

+0.280 
+0.025 

+0.573 

+0.253 
-0.035 
+0.065 
+0.062 
+0.485 

Lac.  8760  

a  Cephei  

Weisse,  562  

57  I2 
-47  27 
—  72  44 
-30    9 
-36  26 

+50  37 

14   22 

Y  Indi 

Fomalhaut  

Lac.  9352  

Brad    3077 

Weisse    175   .    ... 

LI.  46650    .  .  . 

+    I    52 

+26  33 
-37  5i 

Cord.    32416  

326  SPECTROSCOPIC  BINARY  SYSTEMS 

III.  List  of  spectroscopic  binary  systems. 


Name  of  Star. 

Position,  1900. 

Mag. 

Period 
Days. 

Orbital 
Velocity 
km.  sec. 

Authority  or 
Discoverer 

R.A. 

Dec. 

h  m 

0         , 

tj  Andromeda.  . 

o  52 

+22   52 

4.6 

14 

Campbell 

Polaris  

I    22 

+88  46 

2.1 

3-97 

3 

Campbell 

£  Piscium  

I   48 

+   2  42 

4-7 

Campbell 

liCeti  

2      8 

+  8  23 

4-4 

Campbell 

12  Persei  

2    36 

+39  46 

4.9 

Campbell 

T  Persei  

2  47 

+  52    22 

4.0 

Campbell  and  Miss  Maury 

6  Persei  

32 

n     * 

2   87 

Vocel 

X  Tauri  

• 
See 

+  12    12 

"  •  5 

Var. 

4 

Belopolsky 

d  Aurigae  

D3 

5     9 

+45  54 

O.2 

IO4.O 

26 

Campbell  and  Newall 

£  Orionis  

5  27 

—   0  22 

2.4 

1-9 

70 

Deslandres 

ft  Aurigse  

5  52 

+44  56 

2.1 

3.98 

120 

Miss  Maury 

£  Geminor  .... 

6  58 

+20  43 

Var. 

IO.I5 

13 

Belopolsky  and  Campbell 

a1  Geminor.  .  . 

7  28 

+32     7 

2.O 

2.91 

II 

Belopolsky 

A.  G.  C.  10534 

7  55 

-48  50 

5-0 

3.12 

305 

Pickering 

«  Hydrae  

8  42 

+  648 

3-6 

Campbell 

§  Leonis  

9  36 

+  10   21 

3-8 

14-5 

56 

Campbell  and  Miss  Maury 

o  Ursae  Maj  .  .  . 

ii  13 

+32     6 

3-8 

Wright 

93  Leonis  
C  Ursa  Maj  .  .  . 

ii  43+20  46 
13  20+55  27 

4.6 
2.4 

52 

18 
80 

Campbell 
Pickering 

oc.  Virginis  .... 

13  20,  —  10  38 

1.2 

4.01 

91 

Vogel 

C  Centauri  .... 

13  49 

-46  48 

2.7 

8.  02 

Mrs.  Fleming 

d  Bootis  .    .  . 

14.     6 

-1-2  e    04. 

A.    8 

AC\ 

AVritrht 

ft  Lupi 

14       \J 
14    52 

\^*y   j<+ 

4-.  o 
2.8 

4 

Mrs.  Fleming 

£  Librae  

15  19 

—  9  57 

5-2 

240  ± 

13 

Campbell 

it  Scorpii   .  .  . 

3T 

T     C*7 

Miss  Cannon 

6  Draconis  

16    o 

+58  50 

•  l 
4-2 

1  •  D/ 

9 

25 

Campbell 

ft  Herculis  

16  26 

+21    42 

2.8 

12 

Campbell 

fJi  Scorpii  

16  45 

—37  52 

3-6 

1.45 

230 

Bailey 

h  Draconis  .... 

16  55 

+65   17 

4-7 

16 

Campbell 

f  Ursae  Min... 

16  56 

+82    12 

4-5 

25 

Campbell 

ta  Draconis  .  .  . 

17  38 

+68  48 

4.9 

Campbell 

X  Draconis  

18  23 

+72  42 

3-7 

282 

18 

Campbell 

2  Scuti  

18  37 

-99 

6 

Wright 

6  H.  Scuti.... 

18  42 

—  4  51 

4-4 

7 

Wright 

ft  Lyrae  

18  46 

+33  15 

Var. 

12.91 

181 

Belopolsky 

113   Herculis.  . 

18  50 

+22  32 

4-6 

10 

Wright 

v  Sagittarii.  .  . 
77  Aquilae.    .  .  . 

19  16  —  16     8    4.7 
19  47  +  o  45  Var. 

7.18 

20.  6 

Campbell  and  Miss  Maury 
Belopolsky 

o1   Cygni  
ft  Capricorni  .  . 

2O    10 

20  15 

+46  26    3.8 
-15     5    3-4 

looo-j- 

Campbell  and  Miss  Maury 
Campbell  and  Miss  Maury 

a  Equule.i  

21    II 

+  4  50   4-0 

Campbell  and  Miss  Maury 

•K.  Pegasi  

21  40 

+25   ii    4-2 

40 

Campbell 

«  Pegasi  

22      2 

+24  5i    4-0 

10.2 

45 

Campbell 

<5  Cephei  

22   25 

+57  54  Var. 

5-37 

20 

Belopolsky 

77  Pegasi   

22   38 

+29  42    3.1 

818.0 

14 

Campbell 

it  Cephei  
A.  Andromeda. 

23     5 
23  33 

+74  5i    4-5 
+45  56   4-0 

20 

8 

Campbell 
Campbell 

INDEX 


Alcyone,  central  star  of  Pleiades,  79 
Aldebaran,  origin  of  name,  33 
Algol,  variable  star,  101 

type  of,  102 

Al-Sufi  catalogues  the  stars,  43 
Andersen  discovers  new  stars,  132 
Andromeda,  great  nebula  of,  182 
Andromedae,  y,  a  triple  system,  164 
Annular  nebulae,  183 
Apex  of  sun's  motion,  88 

its  position  in  Lyra,  90,  91 

Apical  motions  of  the  stars  denned, 

291 

law  of,  297 

Aqueous  vapour,  lines  of,  66 
Aquilae,  rj,  variable  star,  114 
Arcturus,  rapid  motion  of,  76 
Arequipa  Observatory,  work  of,  23 
Argelander,    his    Durchmusterwjg, 

46,  54 

Argo,  division  of  constellation,  32,  36 
Argus,  Tjy  variable  star,  124 

magnitude  of,  127 

Auriga,  new  star  in,  132 

Aurigae,  <x,  spectroscopic  binary,  168 

Auwers,  new  star  of  1860,  130 

system  of  Sirius,  160 

proper  motions  of  stars,  253 

Bailey,  variable  stars  in  clusters,  173 

stars  in  the  Pleiades,  259 

Barnard,  diffused  nebula   of  Orion, 
187 


Barnard,  photographs  of  Milky  Way, 

268 
Bayer,  his  Uranometria,  33,  44 

system  of  star  names,  33 

Belopolsky,     measures    radial    mo- 
tions, 85 

motion  of  Tf  Aquilae,  86 

Binary  systems,  defined,  157 

of  short  period,  163 

light  and  density  of.   193,  199 

law  of  period,   195 

of  gaseous  density,  200 

spectroscopic,  165 

list  of,  326 

orbits  of,  1 66 

Bond  photographs  stars,  to 
Boss,  apex  of  solar  motion,  88 

proper  motions  of  stars,  254 

Brashear  makes  the   Mills  spectra. 

graph,  12 
Burnham  observes  double  stars,  195 

Campbell,  work  at  Lick  Observatory, 

12 

spectrogram  of  Polaris,  84 

spectrographic  work,  86 

speed  of  solar  motion,  93 

spectrum  of  Nova  Aurigae,   133 

Canopus,  great  luminosity  of,   192 
Cape  Observatory,  activity  of,  8 
Cape  Photographic  Durchmusterung, 

by  Gill,  48 
Capella,  a  binary  system,  168 


327 


3*8 


INDEX. 


Carrigan,  position  of  galaxy,  242 
Castor,  double  star,  158 
Catalogue  of  stars,  defined,  45 
made  by  Hipparchus  and  Ptol- 
emy, 41 

by  Al-Sufi,  42 

by  Ulugh  Beigh,  43 

by  Argelander  and  Schonfeld,  46 

of  nebulae  and  clusters,  179 

Celoria,  star-gauges  of,  248 
Centauri,  a,  the  nearest  star,  146 

orbit  of,  162 

Centauri,  a?,  star-cluster,  173 
Cephei,  5,  variable  star,  115 
Ceti,  o,  variable  star,  early  observa- 
tions, 94 
— —  type  and  period  of,  99 

spectrum  of,  119 

Chandler   catalogues  variable  stars, 

96 
Chase,  search  for  stellar  parallaxes, 

I51 
Clark,  Alvan,  separates   companion 

of  Y  Andromeda,  164 
Clark,  A.  G.,  discovers  companion  of 

Sirius,  161 
Classification,  of  star-spectra,  67 

of  variable  stars,  116 

Clerke,  list  of  new  stars,  173 
Cluster,  Great,  of  Hercules,  171 

of  Perseus,  171 

of  GO  Centauri,  173,  175 

Clusters  of  stars,  169 

variable  stars  in,  173 

gravitation  in,  177 

Collision  theory  of  new  stars,  137 
Colours  of  stars,  supposed  changes  in, 

121 

Coma  Berenices,  cluster  of,  260 
Common,  nebula  of  Orion,  180 
Constellations,  study  of,  28 

how  named,  29 

outlines  of,  not  definite,  31,  35 

Constitution  of  the  stars,  191 


Constitution  of  the  stars,  gaseous, 

206 
Cordoba,  Observatory  of,  origin  and 

work.  6 

Durchmusterung,  47,  55 

Coronas,  T,  new  star  of  1866,  130 

spectrum  of,  130 

Cross  motion  of  stars  defined,  291 

statistics  of,  301 

Crossley  reflector  of  Lick  Obs.,   172 

work  of,  1 86 

Cygni,  Y,  variable  star,  109 

61,  a  binary  system,  159 

parallax   first  determined, 

144 

Dawes  measures  double  stars,  155 
Declination  defined,  39 
Density  of  some  stars,  202 
Distance  of  double  star  defined,  156 
Distribution,  of   the  stars  over  the 

sky,  238 

of  lucid  stars,  240 

of  fainter  stars,  247 

of  proper  motion  stars,  252 

of  fifth  type  stars,  256 

of  stars  in  space,  305 

Double  stars,  defined,  153 
particulars  observed,    155 

See  also  Binary  systems 
Draper  photographs  the  moon,  10 
Dreyer,  catalogue  of  nebulae,  179 
Durchmusterung,  defined,  46 

Argelander's,  46,  54 

SchSnfeld's,  46 

Cordoba,  47 

Cape  Photographic,  48 

counts  of  stars  in,  248 


Easton,  stars  in  Milky  Way,  273 
Elkin,  measures  parallax  of  stars,  149 

triangulates  Pleiades,  170 

Evolution  of  the  stars,  217 


INDEX. 


329 


Fifth  type  stars,  number  and  distrib- 
ution of,  256 

Flamstead  assigns  numbers  to 
stars,  34 

Flint  measures  stellar  parallax,  149 

Galaxy,  crowding  of  stars   toward, 

240,  246 

position  of  circle  of,  242 

belt  of  bright  stars  near,  243 

course  of,   264 

See  also  Milky  Way 
Gill,  his  work  at  the  Cape,  8 
photographs  and  catalogues  the 

stars,  48 

measures  stellar  parallaxes,  149 

Gilliss,  catalogues  southern  stars,   5 
Gould,  founds  Cordoba  Observatory, 

6 
• his   Uranometria  Argentina,    7, 

31 

revises  southern  constellations,  31 

photographs  star-clusters,  47 

distribution  of  stars,  243 

Graham,  zone  of  stars  by,  260 

Halley,  voyage  to  St.  Helena,  4 

catalogues  rj  Argus,  124 

Hartwig,  nature  of  Z  Herculis,  113 
Harvard  Observatory,  work  of,  8 
Heis,  maps  of  lucid  stars,  46 
Herculis,  Z,  variable  star,  113 
Herschel,  J.,  expedition  to  Cape  of 

Good  Hope,  4 

observes  rj  Argus    1 26 

catalogues  nebulae,  180 

Herschel,  W.,  observes  double  stars, 

153 

form  of  the  universe,  233 

Hevelius   forms  new   constellations, 

32 

Hind,  new  star  of  1848,  129 
Hipparchus, supposed  star-catalogue, 

41 


Huggins,  observes  radial  motions,  n 

spectrum  of  T  Coronae,  130 

spectrum  of  nebulae,  188 

life  history  of  the  stars,  219 

Huyghens  observes  nebula  of  Orion, 
178 

Innes,  star  of  greatest  proper  motion, 

77 
magnitude  of  rj  Argus,  127 

Jacoby  measures  photographs,  150 
Johnson  observes  at  St.  Helena,  5 

Kant,  his  antinomies,  228 
Kapteyn,  work  on  Cape  Durchmtts- 

terung,  49 

star  of  greatest  prop,  mot.,  77 

parallaxes  of  stars,  149 

search  for  parallaxes,  150 

mean   parallaxes   of   stars,  291, 

294,  313 

law  of  proper  motions,  291 

Keeler,  annular  nebulae,  184 

number  of  nebulae,  186 

Kelvin,  heat  of  the  sun,  208 
Kempf,  Potsdam  photometry,  24 
Kepler,  new  star  of  1604,  129 
Kepler's  laws  in  binary  systems-  193 
Kirchhoff  s  law,  58 

Lacaille  observes  at  the  Cape,  4 
Lambert,  stellar  system  of,  232 
Lane,  law  of  solar  heat,  210 

limit  of  this  law,  213 

Lick  Observatory,  recent  work  of  12 
Light,  wave-lengths  of,  65,  82 

colours  of,  65 

of  stars,  total,  229 

possible  extinction  of,  in  space, 

231 

Line  of  sight,  motions  in,  81 
Lockyer,  the  meteoritic  hypothesis, 

190 


33° 


INDEX. 


Lyra,  annular  nebula  of,  184 
Lyrae,  ft,  variable  star,  106 

type  of,  108 

constitution  of,  107 

Magellanic  clouds,  stars  in,  256 

Magnitudes  of  stars,  15 

ancient   system   of   designating, 

16 
modern   system  of   designating, 

18,  52 

photographic,  21 

photometric  scale  of,  25 

relation  to  light  of  sun,  26 

possible  changes  in,  121 

Maury,  Miss,  classification  of  spectra, 

72 

Melbourne  Observatory,  5 
Mensurze      Micrometricae,     Struve's, 

154 

Michell,  grouping  of  stars,  169 
Milky  Way,  light  of,  230 

description  of,  264 

rifts  in,  270 

lucid  stars  in,  271 

fainter  stars  in,  273,  275 

possible  distance  of,  316 

Mills   spectrograph,   presented   Lick 

Observatory,  12 

work  with,  86 

Miiller,  Potsdam  photometry,  24 
Myers,  constitution  of  ft  Lyrse,  106 
constitution  of  U  Pegasi,  III 

Names  of  the  stars,  early,  32 
Bayer  system  of,  33 

—  Flamstead  system,  34 

—  list  of  special,  322 
Nebula,  of  Andromeda,  182 
of  Cygnus,  186 

of  Orion,  180 

Omega,  183 

Triphid,  182 

Nebulae,  178 


Nebulae,  spiral,  181 

annular,  183 

planetary,  185 

number  of,  186 

diffused,  187 

distribution  of,  188 

spectrum  of,  188 

vast  extent  of,  188 

constitution  of,  189 

energy  of,  224 

New  star,  of  Tycho,  128 

of  Janson,  129 

of  Kepler,  129 

in  Corona,  130 

in  Auriga,  132 

in  Perseus,  138 

New  stars,  123 
list  of,  128 

rapid  rise  of,  130,  139 

theories  of,  137 

nebular  constitution  of,  138 

Novae,  see  New  stars 

Number,  of  stars,  possible  total    3, 

320 
of  lucid  stars,  52 

Omega  nebula,  183 
Orbit  of  a  Centauri,  162 
Orbits  of  binary  systems,  160 
Orion,  great  nebula  of,  179 

diffused  nebula  of,  187 

—  Trapezium  of,  164 

proper  motions  in,  261 

Orion  type  of  star-spectra,  72 
Oxford  photometry,  24 

Parallactic  motion  of  the  stars,  de- 
nned, 89 

relation  to  parallax,  289 

Parallax,  of  the  stars,  140 

relative  and  absolute,  146 

early  attempts  to  measure,  141 

first  measures  of,  144 

of  a  Centauri,  145,  324 


INDEX. 


33' 


Parallax,  of  61  Cygni,  144,  325 

of  a  Lyrse,  145,  325 

Parallaxes,  list  of,  323 

grouping  of,  307 

mean,  of  Vogel's  stars,  290 

mean,  of  stars  of  different  mag- 
nitudes, 313 

statistics  of,  by  Chase,  151 

Pegasi,  U,  variable  star,  no 
Periods  of  variable  stars,  lengths  of, 

97 
Perseus,  new  star  in,  138 

cluster  of,  170 

Peter  measures  parallaxes   of  stars, 

149 

Photographic  chart  of  the  heavens, 
50 

its  origin,  48 

Photography  of  the  stars,  ro 
Pickering,   E.    C.,   Harvard  photo- 
metry, 23 

period  of  U  Pegasi,  in 

classifies  variable  stars,  116 

law  of  binary  systems,  195 

.         distribution   of   fifth  type  stars, 

256 
Pickering,  W.  H.,  diffused  nebula  of 

Orion,  187 

Pleiades,   their  proper  motion,   79, 
170 

counts  of  stars  in,  259 

Poincare",  revolving  stars,  forms  of, 

112 

Polaris,  spectrogram  of,  84 
Porter,  apex  of  solar  motion,  go 
Position-angle  of  a  double  star,  156 
Potsdam  photometry  of  the  stars,  24 
Praesepe,  star-cluster,  170 

number  of  stars  in,  261 

Pritchard,  photometry  of  the  stars, 
24 

measures  stellar  parallaxes,  159 

Procyon,  orbit  of  companion,  161 
mass  of,  204 


Proper  motions  of  stars,  defined,  75 

measures  of,  76 

mean  speed  of,  299,  304 

components  of,  287 

of  Pleiades,  79 

of  types  I  and  II  compared,  292 

apical  and  cross,  291,  301 

lists  of  greatest,  78,  323 

cases  of  common,  79,  81 

greatest  known,  77 

relation  to  parallax,  312 

Ptolemy,  describes  constellations,  29 

catalogue  of  stars,  41 

Purkinje  phenomenon,  effect  of,  20 

Radial  motions  of  the  stars,  81 
Rayet,  fifth  type  of  spectra,  70 
Rees   measures  Rutherfurd's   photo- 
graphs, 150 

Right  ascension  defined,  39 
Ristenpart,  law  of  proper  motions, 

297 
Ritter   writes   on    gaseous    celestial 

bodies,  210 

Roberts,   A.  W.,  density  of  certain 
stars,  201 

catalogues  variable  stars,  96 

Roberts,    I.,    great    nebula  of   An- 
dromeda, 182 
Rowland,    map   of   solar   spectrum, 

63 

Russell,  density  of  stars,  2O2 
Rutherfurd  photographs  stars,  10 

Schiaparelli,  colour  of  Sirius,  122 
— —  distribution  of  stars,  244 
Schjellerup  translates  Al-Sufi,  42 
Schonfeld  catalogues  the  stars,  46 
Schumann,  ultra-violet  rays,  62 
Secchi,  types  of  stellar  spectra,  67 
See,  colour  of  Sirius,   121 

binary  systems  of  short  period, 

159 
— -  orbit  of  a  Centauri,  162 


332 


INDEX. 


Seeliger,  distribution  of  stars,  247 

progression  in  number  of  stars, 

279 

nature  of  Z  Herculis,  113 

Seven  Stars  (see  Pleiades),  169 
Sidereal  time,  use  of,  40 

Sirius,  light  compared  with  sun,  27 

supposed  change  of  colour  of, 

121 

binary  system  of,  160 

mass  of,  204 

Solar  motion,  speed  of,  92,  303 

apex  of,  88 

South  measures  double  stars,  155 
Spectra  of  the  stars,  56 

classification  of,  67 

Spectrograph  of  Lick  Observatory, 

86 
Spectroscopic   binary  systems,   list 

of,  326 

Spectroscopy,  introduction  of,  9 
Spectrum,  nature  and  definition  of, 

57 

of  gaseous  bodies,  59 

plan  of,  65 

designation  of  lines  in,  63 

description  of,  61 

colours  of,  65,  67 

lines  in,  changed  by  motion,  82 

Spectrum  analysis,  method  of,  58 

canons  of,  59 

Kirchhoff's  law  of,  58 

Spiral  nebulae,  182 

Star  clustering,  law  of,  262 

Star  drift,  81 

Stars,  number  of,  3,  52,  320 

progression  in  number,  277 

-  names  of,  322 

chemical  elements  of,  73 

radial  motions  of,  8 1 

double,  153 

density  of,  202 

gaseous  constitution  of,  206 

heat  of,  how  maintained,  206 


Stars,  light  of,  possible  total,  229,  283 

temperature  of,  215,  278 

triple,  163 

evolution  of,  217 

parallactic  motion  of,  89,  289 

See  also  Double  stars,  Binary  sys- 
tems, Catalogues,  Magnitude, 
Distribution,  Proper  motion. 
Constitution,  Spectra,  Radial 
motions,  New  stars.  Variable 
stars 

Struve,  W.,  measures  double  stars, 
155 

extinction  of  light  in  space,  231 

form  of  the  universe,  234 

Stumpe,  apex  of  solar  motion,  90 

proper  motion  of  the  stars,  296 

Swift  discovers  nebulae,  186 
Sun,  magnitude  of,  as  a  star,  26 

motion   of,  in   space  (see  Solar 

motion),  87 

Taurus,  proper  motions  in,  81 
Tebbut,  magnitude  of  77  Argus,  126 
Thale"n  catalogues  lines  of  iron,  63 
Thome,  Cordoba    Durchmusterung^. 

55 

Trapezium  of  Orion,  164 
Triple  stars,  163 

Tycho  Brahe  catalogues  the  stars,  44 
new  star  of  1572,  128 

Ulugh  Beigh  catalogues  the  stars,  43 
Universe,  extent  of,  228 

in  general  structure  of,  226 

possible  forms  of,  235 

general  conclusions  as  to,  318 

Uranometria  Argentina,  Gould's, 

7,  3i 

Ursa  Major,  motions  of  stars  in,  80 
Ursae  Majoris,  |,  a  binary  system,  167 

Variable  stars,  first  observations,  94. 
classification  of,  95,   116 


INDEX. 


333 


Variable  stars,    periods  of,  97 

periodic,  defined,  96 

light-curve  of,  98,  IO2 

spectra  of,  118 

Algol  type  of,  IO2,  104 

—  ft  Lyrse  type  of,  106 

in  clusters,  173 

catalogued  by  Chandler,  96 

Virginis,  a,  spectroscopic  binary,  165 
Vogel  improves  spectroscopic  meth- 
ods, 12 


Vogel,  classification  of  star  spectra, 

70 
measures  of  radial  motion,  85, 

290 

spectrum  of  Nova  Aurigae,  134 

orbit  of  a  Virginis,  165 

Wave-length  of  light,  how  changed 

by  motion,  82 

Wendell,  variation  of  U  Pegasi,  no 
Wolf,  fifth  type  of  star  spectra,  70 


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DANIEL  G.  BRINTON,  A.M.,  M.D.,  LL.D.,  Sc.D.,  Late  Professor  of 
American  Archaeology  and  Linguistics  in  the  University  of  Pennsyl- 
vania ;  Author  of  "  History  of  Primitive  Religions,"  "  Races  and 
Peoples,"  "  The  American  Race,"  etc.  Edited  by  LIVINGSTON  FAR- 
RAND,  Columbia  University.  8°.  Net,  $1.50  (By  mail,  $1.60.) 

"  Professor  Brinton  his  shown  in  this  volume  an  intimate  and  appreciative  knowledge 
of  all  the  important  anthropological  theories.  No  one  seems  to  have  been  better  acquainted 
with  the  very  great  body  of  facts  represented  by  these  sciences."—  A m.  Journal  of 
Sociology. 

II.— Experiments  on  Animals.  By  STEPHEN  PAGET.  With  an  Intro- 
duction by  Lord  Lister.  Illustrated.  8°.  Net,  $2.00.  (By  mail,  $2.20.) 

44 To  a  large  class  of  readers  this  presentation  will  be  attractive,  since  it  gives  to  them 
in  a  nut-shell  the  meat  of  a  hundred  scientific  dissertations  in  current  periodical  literature. 
The  volume  has  the  authoritative  sanction  of  Lord  Lister." — Boston  Transcript. 

12. — Infection  and  Immunity.  With  Special  Reference  to  the  Prevention 
of  Infectious  Diseases.  By  GEORGE  M.  STERNBERG,  M.D..  LL.D., 
Surgeon-General  U.  S.  Army  (Retired).  Illustrated.  8°.  Net,  $1.75. 
(By  mail,  $1.90.) 

**  A  distinct  public  service  by  an  eminent  authority.  This  admirable  little  work  should 
be  a  part  of  the  prescribed  reading  of  the  head  of  every  institution  in  which  children  or 
youths  are  gathered.  Conspicuously  useful." — tf.  Y.  Times. 

13.— Fatigue.  By  A.  Mosso,  Professor  of  Physiology  in  the  University 
of  Turin.  Translated  by  MARGARET  DRUMMOND,  M.A.,  and  W.  B. 
DRUMMOND,  M.B.,  C.M.,  F.R.C.P.E.,  extra  Physician,  Royal  Hospital 
for  Sick  Children,  Edinburgh;  Author  of  "The  Child,  His  Nature 
and  Nurture."  Illustrated.  8°.  Net,  $1.50. 

"A  book  for  the  student  and  for  the  instructor,  full  of  interest,  also  for  the  intelligent 
general  reader.  The  subject  constitutes  one  of  the  most  fascinating  chapters  i»  *h«  ni»> 
lory  of  medical  science  and  of  philosophical  research  "—Yorkshire  Post. 


14- — Earthquakes.  In  the  Light  of  the  New  Seismology.  By  CLARENCE 
E.  DUTTON,  Major,  U.  S.  A.  Illustrated.  8'.  Net,  $2.00.  (By 
mail,  $2.20  ) 

"  The  book  summarizes  the  results  of  the  men  who  have  accomplished  the  great 
tilings  in  their  pursuit  of  seismological  knowledge.  It  is  abundantly  illustrated  and  il 
fills  a  place  unique  in  the  literature  of  modern  science."— Chicago  Tribune, 

15.— The  Nature  of  Man.  Studies  in  Optimistic  Philosophy.  By  ELI*. 
MKTCHXIKOFF,  Professor  at  the  Pasteur  Institute.  Translation  and 
introduction  by  P.  CHAMBERS  MITCHELL,  M.A.,  D.Sc.  Oxon.  Illus- 
trated. 8°.  Net,  $2.00. 

"A  book  to  be  set  side  by  side  with  Hu«  jy's  Essays,  whose  spirit  it  carries  a  step 
further  on  the  long  road  towards  its  goal.'1 — Mail  and  Express, 

16.— The  Hygiene  of  Nerves  and  Mind  in  Health  and  Disease.  By 
AUGUST  FOKEL,  M.D..  formerly  1'rufessor  of  Psychiatry  in  the  Uni- 
versity of  Zurich.  Authorized  Translation.  8°.  Net,  $2.00.  (By 
mail,  $2.20.) 

A  comprehensive  and  concise  summary  of  the  results  of  science  in  its  chosen  field. 
Its  authorship  is  a  guarantee  that  the  statements  made  are  authoritative  as  far  as  the 
statement  of  an  individual  can  be  so  regarded. 

17.— The  Prolongation  of  Life.    Optimistic  Essays.     By  £LIE  METCH- 
NIKOFT,    Sub-Director   c*   the    Pasteur   Institute.     Author    of    "  The 
Nature  of  Man. "etc.    8°.    Illustrated.     Net,  $2.50.    (By  mail,  $2.70.) 
Popular  Edition.      With  an  introduction  by  Prof.  CHARLES  S.  MlNOT. 
Net,  $1.75. 

In  his  new  work  Professor  Metchnikoff  expounds  at  greater  length,  in  the  light  of 
additional  knowledge  gained  in  the  last  few  years,  his  mam  thesis  that  human  life  is  not 
only  unnaturally  short  but  unnaturally  burdened  with  physical  and  mental  disabilities. 
He  analyzes  the  causes  of  these  disharmonies  and  explains  his  reasons  for  hoping  that 
they  may  be  counteracted  by  a  rational  hygiene. 

18.— The  Solar  System.  A  Study  of  Recent  Observations.  By  Prof. 
CHARLES  LANE  Poo  it,  Professor  of  Astronomy  in  Columbia  University, 
8°.  Illustrated.  Net,  $2.00. 

The  subject  is  presented  in  untechnical  language  and  without  the  use  of  mathematics. 
Professor  Poor  shows  by  what  steps  the  precise  knowledge  of  to-day  has  been  reached  and 
explains  the  marvellous  results  of  modern  methods  and  modern  observations. 

19.— Climate— Considered  Especially  in  Relation  to  Man.  By  ROBERT 
DECOITRCY  WARD,  Assistant  Professor  of  Climatology  in  Harvard 
University.  8°.  Illustrated.  Net,  §2.00. 

This  volume  is  intended  for  persons  who  have  not  had  special  training  in  the  tech- 
nicalities of  climatology.  Climate  covers  a  wholly  different  field  from  that  included  in 
the  meteorological  text-books.  It  handles  bro.td  questions  of  climate  in  a  way  which  has 
not  been  attempted  in  a  single  volume  The  needs  of  the  teacher  and  student  have  been 
kepc  constantly  in  mind. 

20. — Heredity.  By  J.  ARTHUR  THOMSON,  M.A.,  Professor  of  Natural 
History  in  the  University  of  Aberdeen  ;  Author  of  "The  Science  of 
Life."  etc  8°.  Illustrated.  Net,  $3.50. 

The  .-urn  of  this  work  is  to  expound,  in  a  simple  manner,  the  facts  c  f  heredity  and 
inheritance  as  at  present  known,  the  general  conclusions  which  have  been  securely 
establish ed,  and  ihe  more  important  theories  which  have  been  formulated. 

21.— Age,  Growth,  and  Death.  Bv  CHARLES  S.  MINOT,  James  Still- 
•nan  Professor  of  Comparative  Anatomy  in  Harvard  University, 
^resident  of  the  Boston  Society  of  Natural  History,  and  Author  of 
''  Human  Embryology,"  "  A  Laboratory  Text-book  of  Embryology," 
^tc.  8°.  Illustrated. 

This  volume  deals  with  some  of  the  fundamental  problems  of  biology,  and  presents 
a  series  of  "lews  (the  results  of  nearly  thirty  years  of  study.;,  which  the  author  hal 
correlated  for  the  first  time  in  systematic  form. 


22.— The  Interpretation  of  Nature.  By  C.  LLOYD  MORGAN,  LL.D., 
F.K.S.  Crown  8vo.  Net.  $1.25. 

Dr.  Morgan  seeks  to  prove  that  a  belief  in  purpose  as  the  causal  reality  of  which 
nature  is  an  expression  is  not  inconsistent  with  a  full  and  whole-hearted  acceptance  of 
the  explanations  of  naturalism. 

23— Mosquito  Life.  The  Habits  and  Life  Cycles  of  the  Known  Mos- 
quitoes of  the  United  States  ;  Methods  for  their  Control  ;  and  Keys  for 
Ea-y  Identification  of  the  Species  in  their  various  Stages  An  account 
based  on  the  Investigation  of  the  Late  James  William  Ihipree.  Surgeon- 
General  of  Louisiana,  and  upon  the  original  observations  l>y  the  Write;'. 
By  EVELYN  GROESBEF.CK  MITCHELL,  A.B.,  M.S.  With  64  Illustra- 
tions. Crown  8vo.  Net,  $2.00. 

This  volume  has  been  designed  to  meet  the  demand  of  the  constantly  increasing 
number  of  students  for  a  work  presenting  in  compact  form  the  essential  facts  so  far  made 
known  by  scientific  investigation  in  regard  to  the  different  phases  of  this,  as  is  now  con- 
ceded, important  and  highly  interesting  subject.  While  aiming  to  keep  within  reasonable 
bounds,  that  it  may  be  used  for  work  in  the  field  and  in  the  laboratory,  no  portion  of  the 
work  has  been  slighted,  or  fundamental  information  omitted,  in  the  endeavor  to  carry 
this  plan  into  effect. 

24.— Thinking,  Feeling,  Doing.  An  Introduction  to  Mental  Science. 
By  E.  W.  SCRIPTURE,  1'h.D.,  M.D.,  Assistant  Neurologist  Columbia 
University,  formerly  Director  of  the  Psychological  Laboratory  at  Yale 
University.  iS'»  Illustrations.  2d  Edition,  Revised  and  Enlarged. 
Crown  8 vo.  Net,  8' -75- 

"  The  chapters  on  Time  and  Action.  Reaction  Time,  Thinking  Time,  Rhythmic  A  ction, 
and  Power  and  Will  are  most  inte-esttng.  This  book  shouid  be  carefully  read  by  every 
one  who  desires  to  be  famili-ir  with  the  advances  made  in  the  study  of  the  mind,  which 
advances,  in  the  last  twenty-five  years,  have  been  quite  as  striking  and  epoch  making  as 
the  strides  made  in  the  more  material  lines  of  knowledge."— Jour.  Amer.  Mud.  Ass'n, 
Feb.  22,  1908. 

25.— The  World's  Gold.  By  L.  DK  LAUNAY,  Professor  at  the  6cole 
Superieure  des  Mines.  Translated  by  Orlando  Cyprian  Williams. 
With  an  Introduction  by  Charles  A.  Conant,  author  of  "  History  of 
Modern  Banks  of  Issue,"  etcl  Crown  8vo.  Net,  $1.75. 

M.  de  Launay  is  a  professor  of  considerable  repute  not  only  in  France,  but  among 
scientists  throughout  the  world.  In  this  work  he  traces  the  various  uses  and  phases 
of  gold  ;  firstly,  its  geology ;  secondly,  its  extraction ;  thirdly,  its  economic  value. 

26. — The  Interpretation  of  Radium.  By  FREDERICK  SODDY,  Lecturer 
in  Physical  Chemistry  in  the  University  of  Glasgow.  8vo.  With 
Diagrams.  Net,  $1.75. 

As  the  application  of  the  present-day  interpretation  of  Radium  (that  it  is  an  ele- 
ment undergoing  spontaneous  disintegration)  is  not  confined  to  the  physical  sciences, 
but  has  a  wide  and  general  bearing  upon  our  whole  outlook  on  Nature,  Mr.  Soddy  has 
presented  the  subject  in  non-technical  language,  so  that  the  ideas  involved  are  within 
reach  of  the  lay  reader.  No  effort  has  been  spared  to  get  to  the  root  of  the  matter  and 
to  secure  accuracy,  so  that  the  book  should  prove  serviceable  to  other  fields  of  science 
and  investigation,  as  well  as  to  the  general  public. 

In  preparation: 

The  Invisible  Spectrum.  By  Professor  C.  E.  MENDENHALL,  University 
of  Wisconsin. 

The  Physiology  and  Hygiene  of  Exercise.  By  Dr.  G.  L.  MEYLAN, 
Columbia  University. 

Other  volumes  to  be  announced  later. 


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